在一个精确映射到简单自旋1/2伊辛模型的框架下，研究了具有层状磁结构的三维缀饰晶格上自旋1/2和自旋S（S >= 1/2）混合伊辛模型的相变.对于混合自旋的分层伊辛模型，这种映射对应产生了合理的结果，或者通过采用正交晶格上自旋为1/2的伊辛模型的简化解[Z. D. Zhang，Philos.Mag.87（2007）5309-5419]或通过对四重晶格上的相应自旋1/2伊辛模型进行广泛的蒙特卡罗模拟。结果表明，临界行为显着依赖于轴向零场分裂参数，层间和层内相互作用的相对强度。引人注目的自发秩序捕获的“准1D”自旋系统中发现的相互作用参数的限制区域中，零场分裂参数的力量，所有整数值的装饰自旋对他们的“非磁性”的自旋状态。
英文摘要：
Phase transitions of the mixed spin-1/2 and spin-S (S >= 1/2) Ising model on a three-dimensional (3D) decorated lattice with a layered magnetic structure are investigated within the framework of a precise mapping relationship to the simple spin-1/2 Ising model on the tetragonal lattice. This mapping correspondence yields for the layered Ising model of mixed spins plausible results either by adopting the conjectured solution for the spin-1/2 Ising model on the orthorhombic lattice [Z.-D. Zhang, Philos. Mag. 87 (2007) 5309-5419] or by performing extensive Monte Carlo simulations for the corresponding spin-1/2 Ising model on the tetragonal lattice. It is shown that the critical behaviour markedly depends on a relative strength of axial zero-field splitting parameter, inter- and intra-layer interactions. The striking spontaneous order captured to the 'quasi-1D' spin system is found in a restricted region of interaction parameters, where the zero-field splitting parameter forces all integer-valued decorating spins towards their 'non-magnetic' spin state.
A mixed spin-1/2 and spin-3/2 Ising model on a decorated square lattice with a nearest- neighbor interaction, next-nearest-neighbor bilinear interaction, three-site four-spin in- teraction and single-ion anisotropy is exactly investigated using a generalized decoration- iteration transformation, Callen-Suzuki identity and differential operator technique. The ground-state and finite-temperature phase boundaries are obtained by identifying all rel- evant phases corresponding to minimum internal or free energy of the system. The thermal dependencies of magnetization, correlation functions, entrop…
We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting …
We discuss the origin of an enigmatic low-temperature behavior of one-dimensional decorated spin systems which was coined the pseudo-transition. Tracing out the decorated parts results in the standard Ising-chain model with temperature-dependent parameters and the unexpected low-temperature behavior of thermodynamic quantities and correlations of the decorated spin chains can be tracked down to the critical point of the standard Ising-chain model at ${\sf H}=0$ and ${\sf T}=0$. We illustrate this perspective using as examples the spin-1/2 Ising-XYZ diamond chain, the coupled spin-electron doub…
We consider the triangular kagome XXZ-Ising model (TKL XXZ-Ising model) formed by inserting small triangles ("a-trimers") with XXZ spin-1 inside the triangles of the kagome lattice ("b-trimers"). It is a novel mixed spin system and can be solved exactly by transforming into the kagome lattice with the general transformation method for decorated spin systems. In the absence of an external field, we integrate out the quantum spins of the a-trimers and map the TKL model to the kagome Ising model exactly. We obtain the full phase diagram and their zero-temperature entropies (e.g. $s_{max}=5.48895$…
The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing, while the latter one occurs in some paramagnetic phases due to a spin frustration…
The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelas…
Competitive effects of so-called three-site four-spin interactions, single ion anisotropy and bilinear interactions is studied in the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice. Exploring the decoration-iteration transformation, we have obtained exact closed-form expressions for the partition function and other thermodynamic quantities of the model. From these relations, we have numerically determined ground- state and finite-temperature phase diagrams of the system. We have also investigated temperature variations of the correlation functions, internal energy, entropy…
The mixed spin-1/2 and spin-S Ising model on a decorated planar lattice accounting for lattice vibrations of decorating atoms is treated by making use of the canonical coordinate transformation, the decoration-iteration transformation, and the harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective single-ion anisotropy and three-site four-spin interaction, which are responsible for the anomalous spin frustration of the decorating spins in virtue of a competition with the equilibrium nearest-neighbor exchange interaction between the nodal and decorating …
We study the frustration properties of the Ising model on several decorated lattices with arbitrary numbers of decorating spins on all bonds of the lattice within an exact analytical approach based on the Kramers--Wannier transfer-matrix technique. The existence of magnetic frustrations in such situations and their influence on the behavior of the thermodynamic functions of systems is shown. The most important result of our study is related to the description of the possible coexistence of frustrations and long-range magnetic order in partially ordered spin systems.
Exact solution of the mixed-spin Ising model on a decorated square lattice with two different kinds of decorating spins on horizontal and vertical bonds
Phase diagrams and spontaneous magnetization are rigorously calculated for a coupled spin-electron model on a doubly decorated honeycomb lattice, which accounts for a quantum-mechanical hopping of the mobile electrons on decorating sites, the nearest-neighbor Ising coupling between mobile electrons and localized spins, as well as, the further-neighbor Ising coupling between the localized spins placed on nodal sites. The spontaneously ordered ferromagnetic phase, spontaneously ordered antiferromagnetic phase and disordered paramagnetic phase emerge in a phase diagram depending on an electron fi…
Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field
The critical behavior of a hybrid spin-electron model with localized Ising spins placed on nodal sites and mobile electrons delocalized over bonds between two nodal lattice sites is analyzed by the use of a generalized decoration-iteration transformation. Our attention is primarily concentrated on a rigorous analysis of a critical temperature in canonical and grand-canonical statistical ensemble at two particular electron concentrations, corresponding to a quarter ($ρ\!=\!1$) and a half ($ρ\!=\!2$) filled case. It is found that the critical temperature of the investigated spin-electron system …
Paradigm for approaching the forbidden phase transition in the one-dimensional Ising model at fixed finite temperature: Single chain in a magnetic field
The present work clarifies a failure of the effective-field theory in predicting a false spontaneous long-range order and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires with either zero- or one-dimensional magnetic dimensionality. It is conjectured that the standard formulation of the effective-field theory due to Honmura and Kaneyoshi generally predicts for the Ising spin systems a spurious spontaneous long-range order with nonzero critical temperature regardless of their magnetic dimensionality whenever at least one Ising spin has coordination number greater th…
Here we consider the Ising-Heisenberg model in the expanded Kagomé lattice, also known as triangle-dodecagon (3-12) or star lattice. This model can still be understood as a decorated honeycomb lattice. Assuming that the Heisenberg spins are at the vertices of the triangle while other spins are of the Ising type. Thus, this model is equivalent to an effective Kagomé Ising lattice, through the decoration transformation technique. Thus this means that the model is exactly solvable so we can study the most relevant properties of this model. Like the phase diagram at zero temperature, exhibiting a …
Exact evidence for the spontaneous antiferromagnetic long-range order in the two-dimensional hybrid model of localized Ising spins and itinerant electrons
