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arXiv:cond-mat/9510051 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Tricritical universality in a two-dimensional spin fluid

Nigel B. Wilding, P. Nielaba

Published Jan 1, 1996• 109 citations
arXivHTMLPDF

Abstract

Monte Carlo simulations are used to investigate the tricritical point properties of a two-dimensional (2D) spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analaysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2D Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point location are also compared with the simulation measurements. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.53.926

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Monte Carlo simulations are used to investigate the tricritical point properties of a two-dimensional (2D) spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analaysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2D Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point location are also compared with the simulation measurements. \textcopyright{} 1996 The American Physical Society.
The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (Tt{T}_{t}Tt​=0.610\ifmmode\pm\else\textpm\fi{}0.005, Dt{D}_{t}Dt​=1.9655\ifmmode\pm\else\textpm\fi{}0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.
We report on numerical simulations of the two-dimensional spin-1 Blume-Capel ferromagnet embedded in a triangular lattice. Utilizing a range of Monte Carlo and finite-size scaling techniques, we explore several critical aspects along the crystal field–temperature ( Δ , T ) transition line. Wang-Landau simulations measuring the joint density of states in combination with the method of field mixing allow us to probe the phase coexistence curve in high resolution, determining the tricritical point ( Δ t , T t ) with improved accuracy and verifying the tricritical exponents. Extensive multicanonical simulations identifying transition points across the phase diagram characterize the Ising universality class for Δ < Δ t with precise determination of thermal and magnetic critical exponents expected in the second-order regime. On the other hand, for Δ > Δ t , a finite-size scaling analysis is dedicated to revealing the first-order signature in the surface tension that linearly increases upon lowering the temperature deeper into the first-order transition regime. Finally, a comprehensive picture of the phase diagram for the model is presented, collecting transition points obtained from the combined numerical approach in this study and previous estimates in the literature.
We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.
We investigate the location of the critical and tricritical points of the three-dimensional Blume-Capel model by analyzing the behavior of the first Lee-Yang zero, the density of partition function zeros, and higher-order cumulants of the magnetization. Our analysis is conducted through Monte-Carlo simulations, intentionally using only small system sizes. We demonstrate that this approach yields excellent results for studying the critical behavior of the model. Our findings indicate that, at the tricritical point, where logarithmic corrections are anticipated, the numerical results align closely with the theoretical exponents describing these corrections. These expected values are then employed to accurately determine the coordinates of the tricritical point. At the model's critical point, the corrections correspond to those of the three-dimensional Ising model criticality, which we also use to precisely ascertain the critical temperature at zero crystal field. Additionally, we utilize more traditional thermodynamic quantities to validate the self-consistency of our analysis.