低维I中的随机场诱导序
Random Field Induced Order in Low Dimension I
摘要：
考虑经典XY模型中沿Y轴指向的弱随机外场，其强度为$ε$。我们证明了模型定义的$\Z^3$与最近邻耦合表现出剩余磁顺序在水平方向上任意弱的随机场强度，并根据磁场强度，足够低的温度。
英文摘要：
Consider the classical XY model in a weak random external field pointing along the Y axis with strength $ε$. We prove that the model defined on $\Z^3$ with nearest neighbor coupling exhibits residual magnetic order in the horizontal direction for arbitrarily weak random field strengths and, depending on field strength, sufficiently low temperature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
