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Modern Physics Letters B

Ensemble inequivalence in a generalized XY model

Shao-Bo Yu, Ren Xu, Ji-Xuan Hou

Published Jan 10, 2023• 1 citation
Publisher

Abstract

In this paper, we propose a new generalized XY model with nearest-neighbor interaction which cannot be studied analytically. By adopting both the canonical Monte Carlo simulations and the microcanonical Monte Carlo simulations, the first-order phase transitions in both canonical ensemble and microcanonical ensemble are observed numerically, and the accurate phase-transition temperatures of the model with different parameters are given. From the distinct phase diagrams in two different ensembles, we conclude that the model we propose here exists as an ensemble equivalence.

DOI
10.1142/s0217984922502025

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In this paper, we propose a new generalized XY model with nearest-neighbor interaction which cannot be studied analytically. By adopting both the canonical Monte Carlo simulations and the microcanonical Monte Carlo simulations, the first-order phase transitions in both canonical ensemble and microcanonical ensemble are observed numerically, and the accurate phase-transition temperatures of the model with different parameters are given. From the distinct phase diagrams in two different ensembles, we conclude that the model we propose here exists as an ensemble equivalence.
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We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams.
A paradigmatic example of a phase transition taking place in the absence of symmetry-breaking is provided by the Berezinkii-Kosterlitz-Thouless (BKT) transition in the two-dimensional XY model. In the framework of canonical ensemble, this phase transition is defined as an infinite-order one. To the contrary, by tackling the transitional behavior of the two dimensional XY model in the microcanonical ensemble, we show that the BKT phase transition is of second order. This provides a new example of statistical ensemble inequivalence that could apply to a broad class of systems undergoing BKT phase transitions.
Abstract We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range nearest-neighbor (NN) and next-NN couplings which can be either ferromagnetic or antiferromagnetic. Despite the relative simplicity of the model, our calculations in the microcanonical ensemble reveal a rich phase diagram. The comparison with the corresponding phase diagram in the canonical ensemble shows the presence of phase transition points and lines which are different in the two ensembles. As an example, in a region of the phase diagram where the canonical ensemble shows a critical point and a critical end point, the microcanonical ensemble has an additional critical point and also a triple point. The regions of ensemble inequivalence typically occur at lower temperatures and at larger absolute values of the competing couplings. The presence of two free parameters in the model allows us to obtain a fourth-order critical point, which can be fully characterized by deriving its Landau normal form.
In this work the results of the study on a generalization of the XY model with an additional q-fold nematic-like term through Monte Carlo simulations in two dimensions (2D) have been presented. While the conventional 2D XY model has only integer vortexes, the generalized 2D XY model has both integer and non-integer 1/q vortexes, making the phase diagram of the generalized 2D XY model is much richer than that of the conventional 2D XY model. Here, we located the phase transition between the disordered phase (P), the quasi-long-range order phase (F), and the nematic phase (N) for the case of q = 3. We provided the numerical evidence to clarify the N−F phase transition of either the first-ordered or second-ordered phase transition. The results showed that the N−F phase transition is the second-ordered, not the first-order phase transition.