Abstract
The effect of inclusion of higher-order interactions in the XY model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape of the potential, which beyond a certain value leads to the change of the nature of the transition from continuous to first order. The evidence for the first-order transition is provided in the form of the finite-size scaling and the energy histogram analysis. A rough phase diagram is presented as a function of the number of the higher-order interaction terms.
Highlights
The XY spin model is well known to undergo a topological Berezinskii-KosterlitzThouless (BKT) phase transition to a low-temperature quasi-long-range-order (QLRO) phase characterized by an algebraically decaying correlation function [1, 2]
In spite of belonging to the same universality class as the standard XY model, the generalized model changes the character of the transition to the paramagnetic phase to the first-order one for sufficiently large p
Discussion let us briefly discuss the origin of the crossover to the first-order transition regime
Summary
The XY spin model is well known to undergo a topological Berezinskii-KosterlitzThouless (BKT) phase transition to a low-temperature quasi-long-range-order (QLRO) phase characterized by an algebraically decaying correlation function [1, 2]. [3, 4], and references therein) and can play an important role in the system’s behavior. They turned out useful in modeling of certain systems, such as liquid crystals [5, 6], superfluid A phase of 3He [7], and high-temperature cuprate superconductors [8]. These findings resulted in an increased interest in the study of the model with higher-order interactions. The model involving terms up to the p-th order can be described by the Hamiltonian p
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