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

在1996财政年度的研究中，我们通过蒙特卡罗模拟（MCs）发现XY模型在双层三角晶格上的比热有两个峰值。我们已经澄清了两个比热峰中的一个是由于手性的一种奇怪的行为；这是一种新型的相变，发生在一定的相互作用参数范围内，受挫层和未受挫层之间存在竞争。在1997财政年度的研究中，我们研究了新相变的临界现象，通过有限尺寸缩放分析得到α =0.29(9)和β =0.253 (3)；α是比热的临界指数，β是手性急剧变化的临界指数（提交给物理学a，1998年）。为了研究新临界现象的普遍性，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具有反铁磁相互作用，第二层具有铁磁相互作用。我们发现在某些相互作用参数范围内存在相同类型的相变，临界现象的性质与两层三角形晶格中的相变相同（预印本，1998）。我们还研究了四层三角形晶格上的XY模型。四层三角形晶格的结果将在1998年日本物理学会的春季会议上发表。我们研究了两层晶格上的Ising模型的相变性质，因为手性与低温下的Ising自旋具有相同的性质(Physica A,238 (1997) 295；Jpsj,66 (1997) 3053；JPSJ,67（1998）即将出现。为了用一种不同于mc的方法来研究本研究计划中发现的相变的性质，我们为XY模型制定了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年日本物理学会的春季会议上提出。对于多层晶格上的XY模型，我们研究了将系统简化为有限长度的一维系统（提交给physics a，1998）。少

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