Multicritical behavior of the two-dimensional transverse Ising metamagnet in a longitudinal magnetic field

Abstract

Magnetic phenomena of the superantiferromagnetic Ising model in both uniform longitudinal (H) and transverse (Ω) magnetic fields are studied by employing a mean-field variational approach based on Peierls-Bogoliubov inequality for the free energy. A single-spin cluster is used to get the approximate thermodynamic properties of the model. The phase diagrams in the magnetic fields and temperature (T ) planes, namely, H − T and Ω − T , are analyzed on an anisotropic square lattice for some values of the ratio α = J y /J x , where J x and J y are the exchange interactions along the x and y directions, respectively. Depending on the range of the Hamiltonian parameters, one has only second-order transition lines, only first-order transition lines, or first-and second-order transition lines with the presence of tricritical points. The corresponding phase diagrams show no reentrant behavior along the first-order transition lines at low temperatures. These results are different from those obtained by using Effective Field Theory with the same cluster size.

Monte Carlo study of the phase diagram of layered XY antiferromagnet

“…When the strength of the field is increased starting from zero, its phase transition point separating the ordered and disordered phases from each other gets to shift to the lower temperature region. From the theoretical point of view, thermal and magnetic phase transition properties of different kinds of metamagnetic systems have been studied by a wide variety of techniques such as Mean-Field Theory [1][2][3][4][5][6][7][8], Effective-Field Theory [9][10][11][12][13], Monte-Carlo simulation method [14][15][16][17][18][19][20][21][22][23][24][25], and High Temperature Series Expansion method [26,27]. The studies done so far show us that metamagnetic systems can include multicritical points such as tricritical point, bicritical end point and also critical end point depending on the ratio between these ferromagnetic and antiferromagnetic interactions.…”

Effects of trimodal random magnetic field on spin dynamics of quantum Ising chain

“…相变 [1] ，诱导 Ising-like 反铁磁体 BaCo 2 V 2 O 8 发生铁磁-反铁磁相变 [2] ，可以快速 抑制 Ising-like 反铁磁体 SrCo 2 V 2 O 8 的 Né el 温度等 [3] 。在 Ising-like 光学晶格中， 通过改变纵向磁场(纵场)可以引起顺磁-反铁磁相变 [4] 。而横场和纵场共同存 在时的混合磁场(又称倾斜磁场)对自旋系统性质的调控更为明显，研究发现混 合磁场对系统的基态相图 [5,6] 、热力学性质 [7] 、临界行为 [8,9] 、量子相变 [10] 和动力 学行为 [11] 等现象的影响明显不同于外加磁场只有横场或纵场时的结果。 截至目前，对于纯自旋系统已有大量的研究，且 取得了丰硕的成果。但对随 机自旋系统的研究仍然处于发展阶段，这是由于实际材料中的无序效应非常复 杂，有时根本没有规律可循。不同于纯自旋系统，在随机自旋系统中，系统的自 旋-自旋耦合作用或外加磁场不再为常数，而是被取为满足某种概率分布的随机 数。从数学角度来看，随机分布的选取是任意的，常被采用的几种典型随机分布 是离散型的双模分布 [12][13][14][15] 、连续型的高斯分布 [16,17] 和更广义的双高斯分布 [18,19] 等。但从物理角度来看，随机分布的选取还要考虑实际材料的性质。比如晶格中 的非磁性杂质(非磁性自旋、空位或缺陷)不会受到外磁场的影响，且非磁性杂 质的存在会降低系统的随机性等 [20] 。因此可以将纯数学的随机分布进行扩展， 间接引入某些实际因素，例如改变版的双模分布 [21] 、各项异性场依赖的双模分 布 [22] 、对称或非对称的三模随机分布等 [23][24][25] 。 由于三模分布可以蜕化为双模分布，且在特殊参数下(p=1/3)是高斯分布 的一个很好的近似 [26,27] ，因此备受人们关注。一些稀释反铁磁体(如 Fe x Zn 1-x F 2 )， 氰化物晶体(如 X(CN) x Y 1-x )， X =K,Na,Rb，Y=Br,Cl,I)等材料在外磁场下的性质， 可以采用三模分布进行描述 [20,23] 。目前人们对于 Ising 模型在三模型随机外场下…”