【摘要】：本文發(fā)展了一種計(jì)算方法將3維Ising模型的轉(zhuǎn)化矩陣V_1替換為一個(gè)秩更小的轉(zhuǎn)化矩陣.將轉(zhuǎn)化矩陣V_1表示為基矢量的線性疊加,我們發(fā)現(xiàn)可以將基矢量分為幾組,一個(gè)基矢量與V_1的矩陣乘積可以被表示為同組基矢量的線性疊加.以此為原理,我們建立了一個(gè)新的轉(zhuǎn)化矩陣V_2來(lái)描述一個(gè)基矢量和V_1的乘積與同組基矢量之間的關(guān)系,而一組包含基矢量的個(gè)數(shù)就是V_2的秩.V_2的秩比V_1小得多并包含最大特征值.本文用此方法計(jì)算了單位比熱和單位磁矩.結(jié)果顯示存在一對(duì)溫度和磁場(chǎng)的組合使比熱取得最大值,當(dāng)N_1N_2增加時(shí),比熱峰值也增加.
[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.
【作者單位】： 河北省新型功能材料重點(diǎn)實(shí)驗(yàn)室;河北工業(yè)大學(xué)材料學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(編號(hào):51271070) 河北省自然科學(xué)基金(編號(hào):E2014202008,E2016202406) 國(guó)際科技合作計(jì)劃項(xiàng)目(編號(hào):2010DFA51920) 河北省高等學(xué)校科學(xué)技術(shù)研究重點(diǎn)項(xiàng)目(編號(hào):ZH2011202) 河北省新型功能材料重點(diǎn)實(shí)驗(yàn)室資助
【分類(lèi)號(hào)】：O411

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