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-35.64, -32.9, -40.08, -38.32, -37.38, -35.56, -34.36, -33.82, -35.12, -34.96, -35.18, -35.38, -36.54, -33.18, -32.64, -37.26, -37.8, -39.4, -33.58, -37.82, -38.78, -34.38, -34.22, -39.7, -34.34, -33.74, -39.72, -35.08, -38.2, -35.74, -37.44, -33.54, -37.74, -35.68, -36.34, -37.52, -35.28, -33.84, -36.34, -37.54, -34.54, -38.64, -32.54, -36.72, -39.18, -32.1, -35.94, -35.24, -37.3, -35.86, -35.7, -34.34, -34.32, -32.24, -35.3, -35.44, -34.96, -36.66, -36.6, -32.9, -37.26, -41.5, -34.68, -35.04, -33.8, -36.18, -35.84, -36.92, -37.66, -35.0, -41.18, -36.78, -36.12, -35.34, -36.32, -34.88, -32.62, -35.3, -36.88, -33.72, -37.28, -33.28, -35.44, -34.54, -37.64, -41.76, -35.22, -32.86, -32.48, -35.62, -32.62, -33.86, -34.42, -37.18, -35.32, -32.86, -38.82, -34.08, -35.72, -34.82, -39.18, -35.28, -34.74, -32.96, -34.32, -34.24, -33.72, -37.16, -33.9, -34.86, -35.96, -35.78, -34.48, -35.12, -37.08, -36.16, -32.52, -38.74, -35.86, -33.66, -34.44, -29.92, -35.36, -36.6, -37.9, -33.48, -35.38, -34.62, -35.62, -35.48, -36.4, -33.08, -36.08, -35.82, -36.72, -37.58, -34.92, -34.46, -34.46, -34.06, -34.08, -38.58, -33.42, -35.96, -36.62, -35.74, -33.74, -35.02, -34.96, -31.36, -33.46, -37.08, -36.52, -37.56, -38.58, -35.44, -39.66, -37.48, -35.6, -35.14, -37.76, -35.86, -37.08, -37.52, -33.62, -33.34, -36.6, -38.18, -37.94, -32.74, -33.26, -35.18, -35.86, -34.1, -34.58, -34.24, -32.8, -35.68, -34.62, -34.5, -36.62, -35.86, -33.24, -36.52, -32.76, -36.12, -36.34, -33.32, -36.22, -34.24, -34.24, -33.02, -33.98, -35.24, -35.3, -36.62, -39.8, -33.86, -33.36, -37.26, -35.74, -36.18, -36.18, -35.46, -37.84, -38.26, -31.84, -35.26, -31.0, -33.5, -35.34, -37.92, -37.54, -32.86, -37.0, -36.04, -36.76, -35.6, -34.48, -32.64, -39.7, -33.96, -35.74, -36.88, -35.0, -36.32, -32.94, -33.74, -35.1, -36.54, -36.18]
l1=np.array(l1)
l2=np.array(l2)
temp_arr=np.linspace(0.01,20,1000)
#Resampling
smalll1=[]
smalll2=[]
smalltemp=[]
for i in range(len(l1)):
    if i<10 or i%13==0:
        smalll1.append(l1[i])
        smalll2.append(l2[i])
        smalltemp.append(temp_arr[i])
np.where(l1==l1.max())
l1[65]
l2[65]
temp_arr[65]
plt.scatter(smalltemp[:50],smalll1[:50],c="red",s=15,marker="^",label="Monte Carlo Values")
plt.plot(smalltemp[:50],smalll1[:50],linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Specific Heat")
plt.legend()
plt.title("Specific Heat for N=10x10")
plt.savefig("10x10SpecificHeatvsTemp.png",dpi=300)
plt.scatter(smalltemp,smalll2,c="green",s=15,marker="^",label="Monte Carlo Values")
plt.plot(smalltemp,smalll2,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Energy")
plt.title("Energy for N=10x10")
plt.legend(loc="lower right")
plt.savefig("10x10EnergyvsTemp.png",dpi=300)
len(smalll1)<jupyter_output><empty_output><jupyter_text>N=25, 0<T<10 https://www.kaggle.com/siddharthchaini/n-25-sp-heat-0-t-10-100-pts<jupyter_code>tmin=0.01
tmax=10
num_pts=100

temp_arr=np.linspace(tmin,tmax,num_pts)
sp_list = np.array([0.0, 0.0, 0.0, 0.01612460789592163, 0.0, 0.014723839728338284, 0.015922940944167352, 0.046398350898057564, 0.0008623597347354858, 0.0, 0.012282399189561215, 0.0012571428571613887, 0.01336615183997432, 0.0008439544471689621, 0.006415641845889218, 0.003004719727053805, 0.01082143203618952, 0.005240049255999219, 0.011181182934632751, 0.002234946244208364, 0.004213849387260544, 0.004565389745487571, 0.008545516700516054, 0.00766331468235806, 0.00662495175473687, 0.0019294660153397437, 0.0011045840929843967, 0.003586453146222695, 0.0031106037821526044, 0.011625315453998565, 0.005379384518271642, 0.001908721227652934, 0.0011895105848606221, 0.004535637706621494, 0.0009050921369725142, 0.002090532911131375, 0.002290926341841097, 0.0032906439255169645, 0.003718405288707828, 0.003955789589924877, 0.004388712055244715, 0.0023532827557229555, 0.0027281934378228373, 0.0012444656659317329, 0.003764664057569091, 0.0008594097151348604, 0.0010405901781074692, 0.0017991238982142058, 0.002784397487016117, 0.006377468509384374, 0.0016846638648738907, 0.0006909320224962051, 0.0029054684511945184, 0.0010170409504685538, 0.0003481361535377229, 0.0009296413229118855, 0.007416943237576771, 0.002018324369651101, 0.002035170282109758, 0.0015665936942298308, 0.005540526878185637, 0.0021563246023679652, 0.0010042510363748964, 0.0005335679929655903, 0.0011119779587332953, 0.0020879626719300087, 0.0017655603982119996, 0.002561091119697138, 0.0021622381176004536, 0.0005459602338305363, 0.006762433425853945, 0.0011151673800051643, 0.001586559757072242, 0.0034190308439952803, 0.005696177358302276, 0.002882465342376527, 0.011359666152262514, 0.0012664045307655381, 0.002412028141371474, 0.002990487679080074, 0.0018499811985802537, 0.0011950659166264318, 0.0028155407418678463, 0.0012094821082149544, 0.0016451269817819216, 0.00335356385062099, 0.009932422777729719, 0.00041175578652712243, 0.004464381434885337, 0.0026975871655961496, 0.0035802566488677295, 0.0018857780203494136, 0.003600669239129062, 0.0018959724643397493, 0.0006280135685315925, 0.0007003290629482886, 0.0007448022241336807, 0.0008576876513295598, 0.001737356504246952, 0.001176217600000091])
en_list = np.array([-438.0, -392.0, -398.0, -473.12, -396.0, -464.94, -410.48, -404.28, -411.8, -448.0, -341.74, -378.88, -385.26, -355.28, -369.94, -302.02, -314.48, -330.64, -338.5, -309.54, -321.08, -310.16, -300.0, -307.76, -291.44, -303.62, -297.46, -297.28, -302.36, -258.82, -282.62, -309.54, -272.6, -292.42, -289.68, -268.64, -304.98, -271.42, -280.3, -257.44, -238.36, -252.68, -268.26, -248.78, -291.08, -278.34, -255.92, -265.02, -247.06, -248.34, -245.5, -273.28, -244.9, -251.52, -287.66, -256.72, -255.78, -278.96, -264.2, -239.76, -260.04, -231.5, -248.56, -241.2, -255.06, -254.08, -232.26, -235.58, -236.62, -237.5, -224.02, -234.94, -232.82, -236.9, -255.34, -227.14, -257.42, -235.46, -240.9, -242.06, -225.32, -246.24, -231.62, -227.08, -235.48, -226.0, -231.3, -254.02, -216.96, -225.48, -245.82, -221.6, -221.26, -226.58, -243.5, -236.54, -227.16, -234.58, -235.34, -229.92])
polar_list = np.array([0.19999999999999993, 0.25612496949731384, 0.25612496949731384, 0.1442220510185595, 0.25612496949731384, 0.1442220510185595, 0.19999999999999993, 0.19999999999999993, 0.2154065922853801, 0.08944271909999159, 0.25612496949731384, 0.19999999999999993, 0.1442220510185595, 0.25612496949731384, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.1442220510185595, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.1442220510185595, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.1442220510185595, 0.19999999999999993, 0.12841593412720465, 0.1442220510185595, 0.19999999999999993, 0.19999999999999993, 0.1442220510185595, 0.19999999999999993, 0.25941983020403236, 0.19999999999999993, 0.20169472515139175, 0.19999999999999993, 0.25612496949731384, 0.23653013986841387, 0.25612496949731384, 0.17043768703983647, 0.24714497437774363, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.19999999999999993, 0.236481230173254, 0.17713104091760937, 0.19832666153055672, 0.1442220510185595, 0.24040997803806596, 0.20112249938994622, 0.1442220510185595, 0.1955377640814847, 0.25612496949731384, 0.19999999999999993, 0.19999999999999993, 0.25954186208205887, 0.19999999999999993, 0.21178624359443587, 0.19999999999999993, 0.270794284626602, 0.19999999999999993, 0.2246243421422996, 0.28596883263628964, 0.24209372712298535, 0.22244998779892552, 0.25612496949731384, 0.21516471783074706, 0.2289868802857797, 0.2699074560615051, 0.25612496949731384, 0.20841874542459707, 0.25807747954573956, 0.1906287952382346, 0.2151537417642747, 0.24832829202351245, 0.25941983020403225, 0.21122499389946273, 0.2050512472547582, 0.22856664093738752, 0.25707749675356617, 0.26062777090043004, 0.23614623366829285, 0.2370003910941108, 0.216276241154221, 0.2786389765128948, 0.23297399392999515, 0.20743412574434, 0.24827867713060456, 0.26831091881457364, 0.22862373444363002, 0.2132995358259151, 0.22188873810395238, 0.25446591761984755, 0.19999999999999993, 0.25612496949731384, 0.22469498657881812])
#ODD Resampling: Works Well
temp_arr2=[]
sp_list2=[]
en_list2=[]
polar_list2=[]
for i in range(len(temp_arr)):
    if i%2==1:
        temp_arr2.append(temp_arr[i])
        sp_list2.append(sp_list[i])
        en_list2.append(en_list[i])
        polar_list2.append(polar_list[i])
temp_arr=np.array(temp_arr2)
sp_list=np.array(sp_list2)
en_list=np.array(en_list2)
polar_list=np.array(polar_list2)
plt.scatter(temp_arr,sp_list,c="red",s=15,marker="^",label="Monte Carlo Values")
plt.plot(temp_arr,sp_list,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Specific Heat")
plt.legend()
plt.title("Specific Heat for N=25x25")
plt.savefig("25x25SpecificHeatvsTemp.png",dpi=300)
plt.scatter(temp_arr,en_list,c="green",s=15,marker="^",label="Monte Carlo Values")
plt.plot(temp_arr,en_list,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Energy")
plt.legend(loc="lower right")
plt.title("Energy for N=25x25")
plt.savefig("25x25EnergyvsTemp.png",dpi=300)
plt.scatter(temp_arr,polar_list,c="purple",s=15,marker="^",label="Monte Carlo Values")
plt.plot(temp_arr,polar_list,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Polarisation")
plt.legend(loc="lower right")
plt.title("Polarisation for N=25x25")
plt.savefig("25x25PolarisationvsTemp.png",dpi=300)
print(f"Specific Heat Maxima is at temp = {temp_arr[np.where(sp_list==sp_list.max())][0]} K")
print(f"Polarisation Minima is at temp = {temp_arr[np.where(polar_list==polar_list.min())][0]} K")
old=en_list[0]
loc=0
maxjump=0
for i,newen in enumerate(en_list):
    if newen - old >maxjump:
        maxjump=newen - old
        loc=i
    old=newen
print(f"Biggest Energy Jump is at temp = {temp_arr[loc]} K")<jupyter_output>Biggest Energy Jump is at temp = 1.1199999999999999 K<jupyter_text>N=15, 0<T<10 https://www.kaggle.com/siddharthchaini/n-15-sp-heat-0-t-5-100-pts<jupyter_code>tmin=0.01
tmax=10
num_pts=100

temp_arr=np.linspace(tmin,tmax,num_pts)
sp_list = np.array([0.0, 0.0, 0.0, 0.0, 0.0030236605884691415, 0.0165451490771457, 0.0013657729127500638, 0.0, 0.0, 0.005016658497534639, 0.01911047343231801, 0.024221938775497814, 0.02728292354985387, 0.019841232300726316, 0.08948906785706237, 0.04375699108066133, 0.01158623106540979, 0.010076604400833565, 0.017065174526142465, 0.009953387919777432, 0.015504423149356319, 0.034902742195656776, 0.008950198967291633, 0.004259949285125184, 0.006155157655690837, 0.026072029949997855, 0.023513639468038774, 0.014212020506387686, 0.01071358548079586, 0.024157500045263316, 0.012566975035539333, 0.01611956339631539, 0.00840451923207626, 0.00380221592742621, 0.014363388665037653, 0.004250972466422998, 0.007164319607312083, 0.009244187096381628, 0.013274400170890197, 0.005721647660104874, 0.03450340179823146, 0.0032025046250905784, 0.011686589161771815, 0.0025189253413768382, 0.0032027381503454667, 0.008193781613970162, 0.010343184941502192, 0.011932251484804675, 0.006784187817176498, 0.02539111372967089, 0.011662083691698901, 0.014621486257354759, 0.0026567370416449463, 0.0016730612933198027, 0.0019208466377320385, 0.016579772153500386, 0.005614170845855956, 0.0008996377185725621, 0.011310380742104829, 0.0026954871438959194, 0.0024579919719349918, 0.005737244249148219, 0.001932056472403532, 0.0034877929480998013, 0.004057998280433335, 0.003077425378065245, 0.005122036682808025, 0.00955404309197625, 0.00359441624715998, 0.0018754836483429456, 0.006206157098531061, 0.003954489111480465, 0.009171507857141587, 0.0076767849830546115, 0.0032440936059350174, 0.0053357318492376175, 0.003345699429522073, 0.0026316388486873196, 0.010791655545252023, 0.0019841195879593434, 0.0032507269963154145, 0.0015847176055500385, 0.006180598950614566, 0.004765898898600038, 0.003612806739531546, 0.0038477844261453733, 0.0011966782943611367, 0.004728221565927668, 0.0022328817446750676, 0.00249973053776916, 0.0035789696813851, 0.006699834393471014, 0.002570801592814177, 0.004765853293577684, 0.0035006763056537166, 0.0027516791179882263, 0.0015042951988309642, 0.0007070789468105133, 0.0019064413260717974, 0.003080017777777782])
en_list = np.array([-150.0, -176.0, -178.0, -176.0, -177.94, -179.12, -195.94, -174.0, -172.0, -163.22, -155.88, -162.06, -152.36, -138.2, -115.06, -154.38, -141.6, -130.3, -142.18, -149.96, -131.5, -134.04, -117.16, -110.18, -113.5, -118.7, -106.62, -104.22, -94.86, -105.88, -95.66, -115.04, -106.0, -102.42, -89.58, -103.96, -90.7, -106.5, -101.88, -103.0, -80.54, -97.92, -107.16, -92.8, -111.7, -106.24, -91.98, -90.34, -87.02, -90.4, -97.76, -95.64, -87.28, -99.18, -90.8, -91.28, -84.4, -96.8, -85.1, -94.52, -97.14, -85.3, -80.7, -84.38, -90.98, -88.6, -84.78, -86.78, -82.36, -88.94, -91.5, -86.98, -85.64, -83.24, -87.52, -87.88, -81.36, -90.4, -80.18, -81.28, -76.58, -80.02, -88.34, -90.72, -88.76, -85.72, -91.34, -82.14, -80.88, -89.12, -79.34, -90.7, -82.2, -96.4, -88.32, -85.38, -76.54, -79.92, -80.92, -83.86])
polar_list = np.array([0.24037008503093252, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.06666666666666665, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.06666666666666665, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.06666666666666665, 0.06666666666666665, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.19999999999999996, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.188329719708293, 0.14907119849998596, 0.20202455268793496, 0.14907119849998596, 0.14907119849998596, 0.24037008503093252, 0.24037008503093252, 0.12764602022332294, 0.17372189786334155, 0.14907119849998596, 0.14907119849998596, 0.14907119849998596, 0.22447886070579137, 0.17919983105519832, 0.14907119849998596, 0.15181016509591436, 0.14907119849998596, 0.23974346778218528, 0.2548616068352353, 0.16456845581470014, 0.2423292117032678, 0.2803609254186794, 0.13815716887215515, 0.22576226318598105, 0.23671812956969465, 0.20202455268793496, 0.19928558609200656, 0.22522011356423483, 0.2388809243665687, 0.2330661741084568, 0.24783020513279388, 0.23945709616562305, 0.1981711567371978, 0.24605543114401862, 0.22062936622756005, 0.25764880227559767, 0.2356149496731726, 0.23124019637783785, 0.20804673247873798, 0.21422933183603365, 0.19829651244651483, 0.23081441356522509, 0.19751154340527066, 0.25140823464606604, 0.2243239682319136, 0.24395807604557632, 0.2468599339372332, 0.23607716404622142, 0.259384639560546, 0.1801128199205078, 0.2534310187976769, 0.26930519732867864, 0.29491627946225174, 0.27384873251477204, 0.20427878474056238, 0.1746681739640801, 0.23915470647530299, 0.24569365837282572, 0.23140028310210814, 0.2201040601388021, 0.23047625427281598, 0.22028432999412428, 0.2620303048543549, 0.20989365336079932, 0.24032998080413182, 0.1817709315108711, 0.20319563843044336, 0.2499959426173998, 0.29277454031371275, 0.24272942021652752, 0.24758948105475265, 0.20192375612449495])
#EVEN Resampling: Works Well
temp_arr2=[]
sp_list2=[]
en_list2=[]
polar_list2=[]
for i in range(len(temp_arr)):
    if i%2==0:
        temp_arr2.append(temp_arr[i])
        sp_list2.append(sp_list[i])
        en_list2.append(en_list[i])
        polar_list2.append(polar_list[i])
temp_arr=np.array(temp_arr2)
sp_list=np.array(sp_list2)
en_list=np.array(en_list2)
polar_list=np.array(polar_list2)
plt.scatter(temp_arr,sp_list,c="red",s=15,marker="^",label="Monte Carlo Values")
plt.plot(temp_arr,sp_list,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Specific Heat")
plt.legend()
plt.title("Specific Heat for N=15x15")
plt.savefig("15x15SpecificHeatvsTemp.png",dpi=300)
plt.scatter(temp_arr,en_list,c="green",s=15,marker="^",label="Monte Carlo Values")
plt.plot(temp_arr,en_list,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Energy")
plt.legend(loc="lower right")
plt.title("Energy for N=15x15")
plt.savefig("15x15EnergyvsTemp.png",dpi=300)
plt.scatter(temp_arr,polar_list,c="purple",s=15,marker="^",label="Monte Carlo Values")
plt.plot(temp_arr,polar_list,linestyle='dashed')
plt.xlabel("Temperature")
plt.ylabel("Polarisation")
plt.legend(loc="lower right")
plt.title("Polarisation for N=15x15")
plt.savefig("15x15PolarisationvsTemp.png",dpi=300)
print(f"Specific Heat Maxima is at temp = {temp_arr[np.where(sp_list==sp_list.max())][0]} K")
print(f"Polarisation Minima is at temp = {temp_arr[np.where(polar_list==polar_list.min())][0]} K")
old=en_list[0]
loc=0
maxjump=0
for i,newen in enumerate(en_list):
    if newen - old >maxjump:
        maxjump=newen - old
        loc=i
    old=newen
print(f"Biggest Energy Jump is at temp = {temp_arr[loc]} K")<jupyter_output>Biggest Energy Jump is at temp = 1.4227272727272726 K
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