3维有限宽度Ising模型的模拟计算
发布时间：2019-03-09 20:30
【摘要】：本文发展了一种计算方法将3维Ising模型的转化矩阵V_1替换为一个秩更小的转化矩阵.将转化矩阵V_1表示为基矢量的线性叠加,我们发现可以将基矢量分为几组,一个基矢量与V_1的矩阵乘积可以被表示为同组基矢量的线性叠加.以此为原理,我们建立了一个新的转化矩阵V_2来描述一个基矢量和V_1的乘积与同组基矢量之间的关系,而一组包含基矢量的个数就是V_2的秩.V_2的秩比V_1小得多并包含最大特征值.本文用此方法计算了单位比热和单位磁矩.结果显示存在一对温度和磁场的组合使比热取得最大值,当N_1N_2增加时,比热峰值也增加.
[Abstract]:In this paper, a computational method is developed to replace the transformation matrix of the three-dimensional Ising model with a transformation matrix with a smaller rank. We find that the base vector can be divided into several groups, and the matrix product of the base vector and the base vector can be expressed as the linear superposition of the same base vector. Based on this principle, we establish a new transformation matrix (V) 2 to describe the relationship between the product of a base vector and V ~ (?) 1 and the same set of base vectors. The number of base vectors in a group is the rank of V ~ (2), which is much smaller than that of V ~ (?) 1 and contains the maximum eigenvalues. In this paper, the unit specific heat and the unit magnetic moment are calculated by this method. The results show that there is a combination of temperature and magnetic field to maximize the specific heat, and when N_1N_2 increases, the peak value of specific heat also increases.
【作者单位】： 河北省新型功能材料重点实验室;河北工业大学材料学院;
【基金】：国家自然科学基金(编号:51271070) 河北省自然科学基金(编号:E2014202008,E2016202406) 国际科技合作计划项目(编号:2010DFA51920) 河北省高等学校科学技术研究重点项目(编号:ZH2011202) 河北省新型功能材料重点实验室资助
【分类号】：O411
本文编号：2437819
[Abstract]:In this paper, a computational method is developed to replace the transformation matrix of the three-dimensional Ising model with a transformation matrix with a smaller rank. We find that the base vector can be divided into several groups, and the matrix product of the base vector and the base vector can be expressed as the linear superposition of the same base vector. Based on this principle, we establish a new transformation matrix (V) 2 to describe the relationship between the product of a base vector and V ~ (?) 1 and the same set of base vectors. The number of base vectors in a group is the rank of V ~ (2), which is much smaller than that of V ~ (?) 1 and contains the maximum eigenvalues. In this paper, the unit specific heat and the unit magnetic moment are calculated by this method. The results show that there is a combination of temperature and magnetic field to maximize the specific heat, and when N_1N_2 increases, the peak value of specific heat also increases.
【作者单位】： 河北省新型功能材料重点实验室;河北工业大学材料学院;
【基金】：国家自然科学基金(编号:51271070) 河北省自然科学基金(编号:E2014202008,E2016202406) 国际科技合作计划项目(编号:2010DFA51920) 河北省高等学校科学技术研究重点项目(编号:ZH2011202) 河北省新型功能材料重点实验室资助
【分类号】：O411
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