Phase transitions in two planar lattice models and topological defects: A Monte Carlo study

Abstract

Monte Carlo simulation has been performed in the planar P 2 and P 4 models to investigate the effects of the suppression of topological defects on the phase transition exhibited by these models. Suppression of the 1/2-defects on the square plaquettes in the P 2 model leads to complete elimination of the phase transition observed in this model. However in the P 4 model, on suppressing the single 1/2-defects on square plaquettes, the otherwise first order phase transition changes to a second order one which occurs at a higher temperature and this is due to presence of large number of 1/2-pair defects which are left within the square plaquettes. When we suppressed these charges too, complete elimination of phase transition was observed.

Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations

“…1,[3][4][5][6][7][8][9][10][11][12][13][14][15] Here, we examine the nature of the IN phase transition using the Lebwohl-Lasher (LL) model, a minimal lattice LC model whose simplicity has attracted significant research. 4,7,13,14,[16][17][18][19][20][21][22] To the best of our knowledge, the transition mechanism for the LL model has not been studied previously. To do this, we adapt a novel approach for the identification of ordered domains originally proposed in the context of colloidal hard rods by Cuetos and Dijkstra.…”

Homotopy in statistical physics

“…In the nematic n = 3 case, evidence was presented for a transition described by a diverging correlation length and susceptibility but a cusp (as opposed to a divergence) in the specific heat was reported. Similar to the two-dimensional XY case, both the correlation length and the susceptibility appeared [56,60] (n → ∞); BKT or 2 nd -order transition for n = 3 [57,59,61,62]; No transition for n = 4 [65] O(n) 3 n = 2: Z, vortices 2 nd -order transitions (m = 1); n = 3: Z, (see [42] and references therein) monopoles (m = 0); no defects for n 4 RP n−1 3 n = 3 only: Z, 2 nd -order transition [51] (from for n 3 monopoles (m = 0); perturbation theory); n 3: Z2, vortices/ 1 st -order transition [56] (n → ∞); disclinations (m = 1) 1 st -order transition [48,52,53] (n = 3); 1 st -order transition [54,55] (n = 4)…”

“…The powerful conformal techniques used in [20,28,29] were similarly employed in [61], favouring a nematic/isotropic topologically-mediated transition in the two-dimensional RP 2 model and a close similarity with the two-dimensional XY model. The effect of the suppression of the topological defects was explored in [62] where it was demonstrated that the apparent phase transition may be completely eliminated. The suppression is achieved by the introduction of a chemical potential term associated with the defects, making the formation of topological charges energetically expensive.…”

Nematic phase transitions in two-dimensional systems

“…Our own previous contributions [19,20] support the first scenario with QLRO at low temperature like in the XY model, but one cannot exclude a finite -but extremely large -correlation length which exceeds the maximum size available in numerical simulations. A recent study reported extremely convincing new evidence in favour of a topological transition [21], the transition being driven by topologically stable point defects known as 1/2 disclination points. Eventually, in the large−n limit, there is a proof of asymptotic freedom for values of k (in the interaction term (1 + cos θ) k ) which do not exceed a critical k c 4.537 .…”

“…The transition is likely to be driven by a mechanism of condensation of defects, like in the XY model, but due to the local Z 2 symmetry not only usual vortices carrying a charge 1 are stable, but also disclination points carrying charges 1/2 should be stable. The role of these defects might be studied in the way similar to the recent work by Dutta and Roy [21], by the comparison of the transition in the pure model and in a modified version where a chemical potential is artificially introduced in order to control the presence of defects. Now, the observed value of the exponent η at the transition temperature seems to be a bit strange.…”