Aspelmeier T, Wang Wenlong, Moore M A, Katzgraber Helmut G
Felix Bernstein Institute for Mathematical Statistics in the Biosciences, Georg August University of Göttingen, 37077 Göttingen, Germany.
Institute for Mathematical Stochastics, University of Göttingen, 37073 Göttingen, Germany.
Phys Rev E. 2016 Aug;94(2-1):022116. doi: 10.1103/PhysRevE.94.022116. Epub 2016 Aug 11.
The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.
具有幂律长程相互作用的一维伊辛自旋玻璃模型是研究高维空间中自旋玻璃以及寻找自旋玻璃态从具有破缺的复制对称性转变为液滴行为的维度的有用替代模型。为此，我们计算了描述周期性和反周期性边界条件之间自由能差异的指数。进行了数值工作以支持计算中所做的一些假设，并确定相互作用幂律的界面自由能指数的行为。我们关于界面自由能指数的数值结果受到有限尺寸问题的严重影响。
