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理论物理通讯：英文版

Evidence of Invariance of Time Scale at Critical Point in Ising Meanfield Equilibrium Equation of State

Muktish, Acharyya, Ajanta, Bhowal

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

我们解决 Ising 铁磁物质的状态的平衡 meanfield 方程(从 BraggWilliams 获得了理论) 由 NewtonRaphson 方法。重复的数字要求了得到一个会聚的答案(在指定精确性以内) 在任何特别温度，平衡， magnetisation 被观察尽最大努力分叉温度接近批评价值的法律时尚。这作为批评慢下来被识别。代表也被估计。代表的这值与从分析答案获得了那相比。除这以外，数字结果也与展出同意的令人满意的度的一些试验性的结果相比。它从这研究被观察在批评的点的时间规模的不变性的信息在 Ising 铁磁物质的状态的 meanfield 平衡方程是在场的。

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Evidence of Invariance of Time Scale at Critical Point in Ising Meanfield Equilibrium Equation of State

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我们解决 Ising 铁磁物质的状态的平衡 meanfield 方程(从 BraggWilliams 获得了理论) 由 NewtonRaphson 方法。重复的数字要求了得到一个会聚的答案(在指定精确性以内) 在任何特别温度，平衡， magnetisation 被观察尽最大努力分叉温度接近批评价值的法律时尚。这作为批评慢下来被识别。代表也被估计。代表的这值与从分析答案获得了那相比。除这以外，数字结果也与展出同意的令人满意的度的一些试验性的结果相比。它从这研究被观察在批评的点的时间规模的不变性的信息在 Ising 铁磁物质的状态的 meanfield 平衡方程是在场的。
We solve the equilibrium meanfield equation of state of Ising ferromagnet (obtained from Bragg—Williams theory) by Newton—Raphson method. The number of iterations required to get a convergent solution (within a specified accuracy) of equilibrium magnetisation, at any particular temperature, is observed to diverge in a power law fashion as the temperature approaches the critical value. This is identified as the critical slowing down. The exponent is also estimated. This value of the exponent is compared with that obtained from analytic solution. Besides this, the numerical results are also compared with some experimental results exhibiting satisfactory degree of agreement. It is observed from this study that the information of the invariance of time scale at the critical point is present in the meanfield equilibrium equation of state of Ising ferromagnet.
We solved the equilibrium meanfield equation of state of Ising ferromagnet (obtained from Bragg-Williams theory) by Newton-Raphson method. The number of iterations required to get a convergent solution (within a specified accuracy) of equilibrium magnetisation, at any particular temperature, is observed to diverge in a power law fashion as the temperature approaches the critical value. This was identified as the critical slowing down. The exponent is also estimated. This value of the exponent is compared with that obtained from analytic solution. Besides this, the numerical results are also compared with some experimental results exhibiting satisfactory degree of agreement. It is observed from this study that the information of the invariance of time scale at the critical point is present in the meanfield equilibrium equation of state of Ising ferromagnet.
The author presents an investigation of the dynamic critical behaviour near the percolation bicritical point of the 1D bond-diluted Glauber Ising model. The expected bicritical dynamic scaling form is rigorously established for the decay functions describing the decay of the equilibrium wavevector-dependent correlation function and the decay of the magnetisation from a (non-equilibrium) wavevector-dependent initial state. The corresponding characteristic decay times are evaluated exactly and exhibit a cross over from 'pure' to percolation dominated behaviour on increasing the dilution. The results in the percolation regime are in agreement with recent calculations in which domain boundary diffusion methods are applied to a wider class of kinetic Ising models.