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Journal of Advanced Science

A tricritical point of the superconducting phase transformation in the anisotropic charged layered lattice XY model. I.

Morishige Yoneda, Masaaki NIWA, 正三 篠原

Published Jan 1, 1997• 0 citations
Publisher

Abstract

We proposed the anisotropic charged layered XY lattice model for phase transition in high Tc superconducting oxide. It is capable of describing from Kosterlitz-Thouless transition in two dimension to standard second-order phase transition in three dimension. This model is investigated using the mean field plus two loop effective energy approach. We find the tricritical point above Tc that is suggest the possibility of first order phase transition.

DOI
10.2978/jsas.9.1

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We study the crossover between two- and three-dimensional behaviors of the Villain form of the XY spin model on a three-dimensional lattice with anisotropic couplings J1{\mathit{J}}_{1}J1​=J2{\mathit{J}}_{2}J2​=J, J3{\mathit{J}}_{3}J3​=\ensuremath{\alpha}J (0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1). The \ensuremath{\alpha} dependence of various quantities is examined by means of duality transformations, Migdal renormalization group, and Monte Carlo simulations. For the specific heat, a crossover into the Kosterlitz-Thouless behavior takes place around \ensuremath{\alpha}\ensuremath{\simeq}0.2, which corresponds to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{cos}}$\ensuremath{\simeq}0.015 in the cosine form of the XY model. Some implications for models of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductivity are discussed.
Using mean-field theory and high-resolution Monte Carlo simulation technique based on multihistogram method, we have investigated the critical properties of an antiferromagnetic XYXYXY model on the two-dimensional (2D) kagome lattice, with single-ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first-order transition for small values of anisotropy, which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behavior of the system deviates from 2D ${\ensuremath{\phi}}^{6}$ model near the tricritical point. This suggests the possibility for existence of another tricritical universality in two dimensions.
We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane ( J ) and a ferromagnetic plane ( I ), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters ( I , J ), the system presents three phases: namely, a Kosterlitz–Thouless (KT) phase in which the two planes are critical for I predominant over J , a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of ( I , J ): the KT transition, the Ising transition and an XY -Ising transition with ν = 0.849(3). It turns out that the Ising or XY -Ising transition is associated with the disappearance of the chiral order in the Villain plane.
The spin–Peierls phase transition in a quasi-one-dimensional XY chain of S=1/2 of spins interacting through an anisotropic exchange interaction is studied as a function of the degree of anisotropy γ. The spin–Peierls state is described using a mean field theory. As γ increases (small value of the anisotropy), the transition temperature Tc decreases. For intermediate values of the anisotropy parameter γ, a tricritical point separating the regions of first and second order phase transitions is obtained. For larger values of γ, a total suppression of the spin–Peierls state is predicted. Finally, a very unusual temperature dependent gap of the elementary spin excitations is predicted for the anisotropic XY system.