Stability of the universality class of phase transitions against spin interaction variations in the clean two-dimensional square-lattice Ising chain

Taha, Khansaa Y.; Ibrahim, Ahmed K.

doi:10.37652/juaps.2025.164405.1643

	Stability of the universality class of phase transitions against spin interaction variations in the clean two-dimensional square-lattice Ising chain
Journal of University of Anbar for Pure Science
Volume 20, Issue 2, August 2026, Pages 284-294 PDF (1.19 M)
Document Type: Research Paper
DOI: 10.37652/juaps.2025.164405.1643
Authors
Khansaa Y. Taha; Ahmed K. Ibrahim^*
Department of Physics, College of Science, University of Anbar, Ramadi, Anbar, Iraq
Abstract
We perform a comprehensive numerical study of how variations in microscopic coupling strength affect critical behavior in the two-dimensional Ising model. Using extensive Monte Carlo simulations based on the Wolff cluster algorithm, we investigate the clean Ising model on a square lattice for interaction strengths in the range 0.80 ≤ J ≤ 1.20. While the exact solution at J = 1 has long established the model’s critical properties, a systematic numerical assessment of universality under continuous coupling rescaling has not been performed. Here, we address this gap by analyzing systems of linear size L = 20 − 500, allowing for high-precision finite-size scaling of thermodynamic observables. For each coupling, the critical temperature T_C(J) is determined via finite-size extrapolation of the susceptibility maxima, yielding results in quantitative agreement with Onsager’s exact prediction. At the extrapolated critical points, we extract the critical exponents ν, β, γ, and α through detailed scaling analyses. These exponents remain consistent with the exact Ising benchmarks across the full range of interaction strengths, confirming that the universal aspects of the phase transition are preserved. Our findings demonstrate that modifying the microscopic coupling strength rescales the critical temperature without altering the asymptotic critical behavior, thereby providing a clear and quantitative confirmation of the robustness of the two-dimensional Ising universality class.
Keywords
Ising Model; Phase Transitions; Universality Class

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