aqora

Multi-Observable Finite-Size Scaling in the 2D Ising Model and Emergent Thermodynamic Coherence Scale (SCJ Framework)

Baby Sebastian Mundakkttu

We present a high-precision finite-size scaling (FSS) analysis of the two-dimensional Ising model using single-spin Metropolis Monte Carlo simulations on lattice sizes L=12L = 12L=12–128128128. Critical behaviour is characterised through multiple independent observables, including susceptibility peaks, Binder cumulants, and scaling collapse, yielding a consistent estimate of the critical temperature Tc=2.2690(8)T_c = 2.2690(8)Tc=2.2690(8) with excellent agreement to established benchmarks. Temperature-resolved integrated autocorrelation times τint(T) au_{mathrm{int}}(T)τint(T) are computed to account for statistical correlations, demonstrating classical critical slowing down with scaling τint∝Lz au_{mathrm{int}} propto L^zτint∝Lz, where z≈2.1z approx 2.1z≈2.1. All uncertainties are corrected using correlation-aware error propagation. Building on these results, we introduce a Scale–Coherence Junction (SCJ) interpretation, defining a thermodynamic coherence energy scale: E_coh = k_B * T_c This provides a phenomenological bridge between critical phenomena and coherence thresholds, suggesting that maximal system-wide correlations at criticality correspond to enhanced sensitivity to environmental interactions.We present a high-precision finite-size scaling (FSS) analysis of the two-dimensional Ising model using single-spin Metropolis Monte Carlo simulations on lattice sizes L=12L = 12L=12–128128128. Critical behaviour is characterised through multiple independent observables, including susceptibility peaks, Binder cumulants, and scaling collapse, yielding a consistent estimate of the critical temperature Tc=2.2690(8)T_c = 2.2690(8)Tc=2.2690(8) with excellent agreement to established benchmarks. Temperature-resolved integrated autocorrelation times τint(T) au_{mathrm{int}}(T)τint(T) are computed to account for statistical correlations, demonstrating classical critical slowing down with scaling τint∝Lz au_{mathrm{int}} propto L^zτint∝Lz, where z≈2.1z approx 2.1z≈2.1. All uncertainties are corrected using correlation-aware error propagation. Building on these results, we introduce a Scale–Coherence Junction (SCJ) interpretation, defining a thermodynamic coherence energy scale: E_coh = k_B * T_c This provides a phenomenological bridge between critical phenomena and coherence thresholds, suggesting that maximal system-wide correlations at criticality correspond to enhanced sensitivity to environmental interactions.

JOURNAL OF ADVANCE AND FUTURE RESEARCHApr 1, 20260 citations

縮退度及び相互作用の対称性と相転移の次数 (統計力学の数学的問題(基研研究会報告))

藤生中野

る消滅演算子 O また,別に線形応答理論を使って ∞

物性研究Feb 20, 19750 citations

量子ゲート平均忠実度測定方法としての Randomized Benchmarking の有効性と課題 (量子統計モデリングのための基盤構築)

貴大角田

数理解析研究所講究録Jan 1, 20170 citations

非エルミート・ランダムハイゼンベルク鎖の準位統計(基礎物理学研究所短期研究会「量子効果が顕著な役割を果たす磁性現象の新展開」,研究会報告)

浩一草部, 恵子千原, 隆司平井

物性研究Sep 20, 19990 citations

非エルミート・ランダムハイゼンベルク鎖の準位統計(基礎物理学研究所短期研究会「量子効果が顕著な役割を果たす磁性現象の新展開」,研究会報告)