STUDY ON CRITICAL PHENOMENA OF LAYERED XY MODEL WITH COMPETING INTERACTIONS BY MONTE CARLO SIMULATIONS

具有竞争相互作用的分层XY模型关键现象的蒙特卡罗模拟研究

• 批准号: 08640472
• 负责人: HORIGUCHI Tsuyoshi
• 金额: $ 1.28万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640472/
• 关键词: layred magnet; XY model; KT transition; chirality transition; Monte Carlo simulations; finite size scaling; Ising model; frustration; 有限シズスケーリング

In the research done in the fiscal year of 1996, we have found that there are two peaks in the specific heat for an XY model on a two-layr triangular lattice by Monte Carlo simulations (MCs). We have clarified that one of two peaks of the specific heat is due to a strange behavior of the chirality ; this is a new type of phase transition and occurs in some range of interaction parameters where there is a competition between the frustrated layr and the unfrustrated layr. In the research done in the fiscal year of 1997, we have investigated the critical phenomena for the new phase transition and found alpha=0.29 (9) and beta=0.253 (3) by means of finite size scaling analyzes ; alpha is the critical exponent for the specific heat and beta is the one for a steep change of the chirality (submitted to Physica A,1998). In order to investigate a universality of the new critical phenomena, we have investigated the XY model on a three-layr triangular lattice in which the first layr and the third … More layr have an antiferromagnetic interaction and the second layr has a ferromagnetic interaction. We have found the same type of phase transition in some range of interaction parameters and the nature of the critical phenomena is the same as that in the two-layr triangular lattice (preprint, 1998). We have also investigated the XY model on a four-layr triangular lattice. The results for four-layr triangular lattice will be presented in the 1998 spring-meeting of the Physical Society of Japan.We have investigated the nature of phase transition for the Ising model on two-layr lattices, since the chirality has the same nature as the Ising spin in the low-temperature (Physica A,238 (1997) 295 ; JPSJ,66 (1997) 3053 ; JPSJ,67 (1998) to appear). In order to investigate the nature of the phase transition found in the present research proposal by a different approach from MCs, we have formulated the density matrix renormalization group method for the XY model (PRE,56 (1997) 3920). Its application to the two-layr XY model will be presented in the 1998 spring-meeting of the Physical Society of Japan. For an XY model on many-layr lattice, we have investigated the system reduced to a one-dimensional system of finite length (submitted to Physica A,1998). Less

在1996财政年度的研究中，我们用MonteCarlo模拟（MC）发现双层三角晶格上XY模型的比热有两个峰值。我们已经澄清，比热的两个峰值之一是由于一个奇怪的行为的手征，这是一种新型的相变，并发生在一定范围内的相互作用参数，其中有一个竞争之间的挫折layr和unfrustrated layr。在1997财政年度的研究中，我们研究了新相变的临界现象，并通过有限尺寸标度分析发现α =0.29（9）和β =0.253（3）; α是比热的临界指数，β是手性急剧变化的指数（提交给Physica A，1998）。为了研究这种新的临界现象的普遍性，我们研究了三层三角形晶格上的XY模型，其中第一层和第三层分别为 ...更多信息 层R具有反铁磁相互作用，第二层R具有铁磁相互作用。在一定的相互作用参数范围内，我们发现了相同类型的相变，临界现象的性质与双层三角晶格中的临界现象相同（预印本，1998）。我们还研究了四层三角晶格上的XY模型。四层三角晶格的结果将在1998年日本物理学会春季会议上发表。我们研究了双层晶格上Ising模型的相变性质，因为在低温下手征性与Ising自旋具有相同的性质（Physica A，238（1997）295 ; JPSJ，66（1997）3053 ; JPSJ，67（1998）待发表）。为了用不同于MCs的方法研究本研究方案中发现的相变的性质，我们制定了XY模型的密度矩阵重整化群方法（PRE，56（1997）3920）。它在两层XY模型中的应用将在1998年日本物理学会春季会议上提出。对于多层晶格上的XY模型，我们将其简化为一维有限长系统（提交给Physica A，1998）。少

项目成果

T.Horiguchi and N.Tsushima: "Shift exponent and breakdown of universality for the two-layr Ising model on a square lattice" Physica A. 238. 295-306 (1997)

T.Horiguchi 和 N.Tsushima：“方格上两层伊辛模型的位移指数和普适性分解”Physica A. 238. 295-306 (1997)

本田泰・堀口剛: "Critical phase of magnetic hard hexagon model on a triangular lattice" Phys.Rev.E. 55・1. 194-198 (1997)

Yasushi Honda 和 Tsuyoshi Horiguchi：“三角晶格上的磁性硬六边形模型的临界相”Phys.Rev.E 194-198（1997）。

本田 泰・堀口 剛: "Density-matrix renormalization group for the…" Phys.Reu.E. 56. 3920-3926 (1997)

Yasushi Honda 和 Tsuyoshi Horiguchi：“密度矩阵重正化群……” Phys.Reu.E 56. 3920-3926 (1997)

本田 泰・堀口 剛: "Density-matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model" Physical Review E. 56. 3920-3926 (1997)

Yasushi Honda 和 Tsuyoshi Horiguchi：“19 顶点模型的 Berezinskii-Kosterlitz-Thouless 过渡的密度矩阵重整化群”《物理评论》E. 56. 3920-3926 (1997)

N.Tsushima, Y Honda and T.Horiguchi: "Phase diagram of spin-3/2 Ising modelon a square lattice in terms of corner transfer matrix renormalization group method" J.Phys.Soc.Japan. 67, (in printing). (1998)

N.Tsushima、Y Honda 和 T.Horiguchi：“根据角传递矩阵重整化群方法在方晶格上自旋 3/2 Ising 模型的相图”J.Phys.Soc.Japan。