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Physica A Statistical Mechanics and its Applications

Critical finite-size scaling of magnetization distribution function for Baxter–Wu model

S.S. Martinos, Anastasios Malakis, Ioannis A. Hadjiagapiou

Published Oct 25, 2003• 12 citations
Publisher
DOI
10.1016/j.physa.2003.09.057

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Our research focuses on the creation of a 3D layered system model that adheres to a three-spin Baxter–Wu-like interaction. To address the phase transition problem, we use entropic sampling simulations to construct the density of states and analyze various quantities such as the total magnetization, average energy, magnetic susceptibility, energy probability distribution function, and inverse microcanonical temperature. Once we established that the system undergoes a first-order phase transition, we carried out a finite-size scaling procedure by carefully studying the critical behavior of the minimum temperature of cumulants for energy and magnetization. We also computed the pseudocritical temperature, Tc(L), which is the temperature where the energy density probability distribution has a double peak. Based on our analysis, we were able to obtain an estimation of the transition temperature as Tc≈3.94 and the latent heat value ΔE≈1.2 at this point.

•Jan 1, 2025•0 citations
The finite size scaling method is used to study the critical properties of the spin-1 Baxter-Wu model as function of the fugacity, z, of the vacant (spin zero) sites. For z=0, the thermal exponent converges very quickly to the (exact) value y t =3/2. For z>0, y t monotonically increases beyond the value 2. This increase is interpreted as indicating a first-order transition. Out of several possible renormalisation group flows, the results seem to favour the one in which the critical Baxter-Wu Hamiltonian flows to the fixed point of the 4-state Potts model, with the amplitude of the marginal operator equal to zero.
Our research focuses on the creation of a 3D layered system model that adheres to a three-spin Baxter–Wu-like interaction. To address the phase transition problem, we use entropic sampling simulations to construct the density of states and analyze various quantities such as the total magnetization, average energy, magnetic susceptibility, energy probability distribution function, and inverse microcanonical temperature. Once we established that the system undergoes a first-order phase transition, we carried out a finite-size scaling procedure by carefully studying the critical behavior of the minimum temperature of cumulants for energy and magnetization. We also computed the pseudocritical temperature, Tc(L), which is the temperature where the energy density probability distribution has a double peak. Based on our analysis, we were able to obtain an estimation of the transition temperature as Tc≈3.94 and the latent heat value ΔE≈1.2 at this point.