Nematic phase transitions in two-dimensional systems

Abstract

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterized by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial P 4 . The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles or correlation functions. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results, while the value of the correlation function exponent at the deconfining transition seems controversial. : 05.40.+j, 64.60.Fr, 75.10.Hk Key words: liquid crystal, orientational transition, nematic phase, topological transition PACS Ordering in two dimensionsIn the context of phase transitions, two-dimensional models exhibit a very rich variety of typical behaviours, ranging from conventional temperature-driven second order phase transitions (e.g. Ising model) to first-order ones (e.g. q > 4-state Potts model), with specific properties of models having continuous global symmetry which may present defect-mediated topological phase transitions (e.g. XY model) or even no transition at all (e.g. Heisenberg model). Models of nematic-isotropic orientational phase transitions belong to this latter category of systems displaying a continuous symmetry. Ordering in low dimensional systems is likely to be frustrated by the strength of fluctuations. On qualitative grounds, let us consider for instance *

On the critical behaviour of two-dimensional liquid crystals

“…The situation is clear in the case of planar rotator models (see e.g. references [27,28]), but still controversial for three-component models. In reference [27], we have studied the nematic-isotropic transition of 2D liquid crystals using a O(2) vector model characterized by nonlinear nearest-neighbour spin interactions governed by the fourth Legendre polynomial P 4 .…”

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

“…Such long-range decay in the case of the free (nematic) system indicates the presence of orientationally ordered nematic domains in the system. 58,59 When looked at carefully, such nematic domains are visible in the snapshot in Fig. 1(a).…”

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“…Ref. [14] in a similar context.). The recent works of S. T. Bramwell et al [13,15,16] give deep analysis of the magnetisation probability distribution which they claim to be non-Gaussian and of universal form, independent of both system size and critical exponent η reg .…”