First-order transitions for some generalizedXYmodels

Abstract

In this letter we demonstrate the occurrence of first-order transitions in temperature for some recently introduced generalized XY models, and also point out the connection between them and annealed site-diluted (lattice-gas) continuous-spin models.

First-order phase transitions in classical lattice gas spin models

“…PR was further studied for =−3D / 4, where evidence of a first-order transition was found. The change of the nature of the phase transition from BKT to a discontinuous one agrees with previous RG predictions 23,24 and rigorous mathematical results; 22 on the other hand, in recent simulation studies of quenched dilution it was found that the transition temperature vanishes below the percolation threshold. [28][29][30][31] Notice that usage of the grand-canonical ensemble allows quite wide changes of density with temperature.…”

Berezinskii–Kosterlitz–Thouless phase transition of 2D dilute generalized model

“…In turn, different techniques, such as self-consistent harmonic approximation (SCHA) and Monte Carlo (MC) simulation, have been used to study this transition when q > 1. It was found that the BKT critical temperature decreases as q increases and this model was proved to be the same universality class as the usual XY model [7,9,10,8]. Once the BKT transition appears, the vortex pair density starts to grow simultaneously.…”

“…would be an interesting question. Several methods mentioned in a number of the references may be helpful in finding a solution to this problem [7,8,[42][43][44].…”

“…Their Hamiltonian was defined as follows [6] H G xy = −J i,j (sin θ i sin θ j ) q cos(ϕ i − ϕ j ), (1) where spin vector S i = (S x i , S y i , S z i ) = (sin θ i cos ϕ i , sin θ i sin ϕ i , cos θ i ), q ∈ N is the generalization parameter. A first order phase transition was expected in this model when a large value of q was reached [7,8]. This model was first studied by the mean field and two-site cluster approach in order to support a BKT phase transition taking place at finite temperature when 3D [6].…”

Monte Carlo study of the two-dimensional vector Blume-Capel model

“…͑2͔͒, and three-component spins which are coupled anisotropically. [28][29][30][31][32][33][34] A set of studies have put forward strong evidence that, although the introduction of vacancies does cause a region of first-order phase transitions to occur, it does not alter the Kosterlitz-Thouless ͑KT͒ critical behavior in other regions of parameter space. 35 In work on the phase diagram of three-dimensional systems, it has been argued that the elucidation of the properties of the VBCM is important to an understanding of experiments on 3 He-4 He mixtures confined between two walls.…”