Critical exponents and unusual properties of the broken phase in the 3d-RP2 antiferromagnetic model
We present the results of a Monte Carlo simulation of the antiferromagnetic RP^2 model in three dimensions. 
With finite-size scaling techniques we accurately measure the critical exponents and compare them with those of 
O(N) models. We are able to parameterize the corrections-to-scaling. The symmetry properties of the broken 
phase are also studied.
Mean field and computer simulation study of a nematogenic lattice model including three-body interactions
Abstract By now, nematogenic lattice models have been extensively studied in the literature dealing with liquid crystals; they usually involve cylindrically symmetric (uniaxial) particles and pairwise additive interaction potentials. On the other hand, quantum mechanical perturbation theory shows that interatomic or intermolecular potentials are only approximately pairwise additive; the pairwise additivity approximation (PAA) of molecular interactions has been extensively and systematically used in the statistical mechanics of condensed matter, and has proven rather successful. As an attempt to move beyond the PAA in the simulation of mesogenic systems, we have considered here a nematogenic lattice model consisting of uniaxial particles, whose centres of mass are associated with a simple-cubic lattice, and whose interaction potentials consist of a pairwise additive dispersion (Nehring–Saupe) term, restricted to nearest neighbours (and already studied in the literature), plus a short-range triplet-additive one, i.e., the Kielich–Stogryn generalization of the Axilrod–Teller–Muto formula for three atoms. The model has been studied by Mean Field theory and Monte Carlo simulation; the three-body term was found to produce a recognizable quantitative effect on the nematic ordering transition.
A renormalization-group study of helimagnets in D = 2 + ϵ dimensions
Abstract The nonlinear sigma model O(N) ⊗ O(2)/O(N − 2) ⊗ O (2) describing the phase transition of N-component helimagnets is built and studied up to two-loop order in D = 2 + ϵ dimensions. It is shown that a stable fixed point exists as soon as N is greater than 3 (or equal) in the neighborhood of two dimensions. The critical exponents ν and η are obtained. In the N = 3 case, the symmetry of the system is dynamically enlarged at the fixed point from O(3) ⊗ O(2)/O(2) to O(3) × O(3)/O(3) ∼ O(4)/O(3). We show that the order parameter for Heisenberg helimagnets involves a tensor representation of O(4) and we verify it explicitly at one-loop order on the value of the exponents. We show that for large N and in the neighborhood of two dimensions this nonlinear sigma model describes the same critical theory as the Landau-Ginzburg linear theory. As a consequence, the critical behavior evolves smoothly between D = 2 and D = 4 dimensions in this limit. However taking into account the old results from the D = 4 − ϵ expansion of the linear theory, we show that most likely the nature of the transition must change between D = 2 and D = 4 dimensions for sufficiently small N (including N = 3). The simplest possibility is that there exists a dividing line Nc(D) in the plane (N, D) separating a first-order region containing the Heisenberg point at D = 4 and a second-order region containing the whole D = 2 axis. We conclude that the phase transition of Heisenberg helimagnets in dimension 3 is either first order or second order with O(4) exponents involving a tensor representation or tricritical with mean-field exponents.