One-dimensional ising model with next-nearest-neighbour interaction in magnetic field

The exact solution for the one-dimensional Ising model with nearest-neighbour and next-nearest-neighbour interactions in an external magnetic field is obtained within the framework of the Kramers-Wannier transfer matrix. The explicit analytical expressions for thermodynamic quantities such as magnetization, magnetic susceptibility and specific heat are derived and analyzed at length as functions of temperature, magnetic field, and the signs and values of the interaction parameters.     

Nearest neighbor ising model with added local 4-spin interaction

The effects of adding a local 4-spin term to the nearest neighbor Ising model are studied. The relevant parameter isx, the ratio of the four- to the two-spin interaction strength. We have evaluated the first six terms of the high temperature susceptibility expansion and found them to be consistent with the value 1.75 of the critical exponent γ. The critical exponent α is shown to remain zero to first order inx, provided that the free energy is analytic inx. We also demonstrate the equivalence of the model examined to an elastic spin system with pure two-spin interactions.     

Two-component ising chain with nearest-neighbor interaction

The one-dimensional, two-component linear Ising chain with nearest-neighbor interaction is formulated by using the transfer matrix method, with emphasis placed on the case in which the two components are randomly distributed along the chain. Certain recurrence formulas appear such that themth-order partition function of one of the components is dependent on the lower-order ones. The algorithm provides a working basis for discussing the thermodynamic and magnetic functions with various concentrations of one of the components. An exact expression for the partition function is derived for a linear chain which is composed of a periodic distribution of the two components. The construction of a periodic sequence which would approximate a random distribution of the two components is briefly discussed.This study was partially supported by ARPA and monitored by ONR(N00014-17-0308).     

Quantum spin liquid in interacting Kane-Mele model with staggered on-site potential

In this paper, we mainly study the magnetic properties of the interacting Kane-Mele model with staggered on-site potential. Due to the absence of spin rotation symmetry, there exists a spin anisotropic energy term in the effective nonlinear σ model (NLσM). Based on the NLσM with spin anisotropic energy term, we derive a complex phase diagram and find that there exist quantum spin liquid states at the moderate coupling region.     

Exact renormalization transformation for the one-dimensional ising model with finite range interaction

The transfer matrix formalism is employed in order to construct the exact renormalization transformation for the one-dimensional Ising model with finite range interaction. The method is applied to the nearest-neighbour model and to the next nearest-neighbour model.     

Quantum field model with unrenormalizable interaction

The unitary relativistic model of quantum field theory with rapidly increasing spectral function (i.e. it grows faster than any finite power of momentum) is investigated. It is shown that there exist nontrivial Lagrangians, leading to this kind of spectral functions and allowing to construct the local theory without the ultraviolet divergences on their basis. In this theory theS-matrix is unitary and not equal identically to unity.     

Nonplanar two-dimensional ising model with short range two-spin interaction showing continuously variable critical exponents

The relation between a bond decorated Union Jack lattice with short range two-spin interactions and the sixteen- and eight-vertex model is pointed out. It is shown that a special case of that model maps to the spin equivalent of Baxter's model. Thus we have an example where the critical exponents depend continuously on the values of the coupling constants in contrast to naive universality so far assumed to be valid for such a model. This rigorously proves that naive universality is not necessarily valid for 2d Ising models with short range two-spin interactions whereas a weaker form of universality due to Suzuki seems to hold.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

The general ising model

Harmonic analysis and the generalized GKS inequalities are applied to examine features of the general Ising model.     

One-dimensional kinetic ising model with one impurity

The effect of one impurity with arbitrary temperature independent relaxation time on the one-dimensional kinetic Ising model is exactly studied. The dynamical susceptibility for the low concentration of defect is also obtained.Work partially by CNPq and FINEP (Brazilian Agencies). A preliminary version of this paper has been presented at the 15th International Conference on Thermodynamics and Statistical Mechanics, Edinburgh, 1983     

Decorated ising model with classical vector spins

A decorated Ising model with classical vector spins on a square lattice is investigated in detail. The partition function is reduced to the one of the Ising model with effective exchange integrals. Three successive phase-transition temperatures are obtained and four states, namely, paramagnetic, antiferromagnetic, again paramagnetic and ferromagnetic states are realized as the temperature is decreased. For systems on other two- and three-dimensional loose-packed lattices, the situation is the same as the system on the square lattice.     

Quantum dimer model on the kagome lattice: solvable dimer-liquid and ising gauge theory

We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices include the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimer liquid. These models offer a very natural-and maybe the simplest possible-framework to illustrate general concepts such as fractionalization, topological order, and relation to Z2 gauge theories.     

Quantum binding of the BCS interaction model

The Schrödinger (as opposed to the Cooper or BCS-gap) equation is solved without approximation in momentum space for the BCS interaction model to obtain the quantum bound-state spectrum of an isolated pair of fermions in one, two, and three dimensions. Regardless of dimensionality, there is never more than a single bound state (in analogy with the nucleon-nucleon interaction), but a threshold value of the potential strength is needed to support this state in any dimension. For very low densities one recovers previously known formulas for two and three dimensions which are consistent in this limit with the more familiar properties of quantum binding for simple, purely attractive wells. Results are illustrated for typical conventional, cuprate, and superconducting semiconductors having controversially low carrier densities.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq=Σ _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q≠0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins η _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i ?η _i can be interpreted as clusters with an internal degree of freedom. The specific heat Δc and the susceptibility Δ_χ of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat Δc is an analytic function over the whole temperature range and the susceptibility Δ_χ shows a cusp at the transition temperatureT _c of the basic system.     

Mixed-spin ising model with one- and two-spin competing dynamics

In this work we found the stationary states of a kinetic Ising model, with two different types of spins: sigma=1/2 and S=1. We divided the spins into two interpenetrating sublattices, and found the time evolution for the probability of the states of the system. We employed two transition rates which compete between themselves: one, associated with the Glauber process, which describes the relaxation of the system through one-spin flips; the other, related to the simultaneous flipping of pairs of neighboring spins, simulates an input of energy into the system. Using the dynamical pair approximation, we determined the equations of motion for the sublattice magnetizations, and also for the correlation function between first neighbors. We found the phase diagram for the stationary states of the model, and we showed that it exhibits two continuous transition lines: one line between the ferrimagnetic and paramagnetic phases, and the other between the paramagnetic and antiferrimagnetic phases.     

Two-dimensional ising models with competing interaction—a Monte Carlo study

Two-dimensional Ising models on a square lattice with competing interactions along one axis or both axes are studied primarily by the Monte Carlo method. Several commensurate-incommensurate transitions are found. Dislocation-like configurations are identified near the sinusoidal — paramagnetic transition in accordance with the idea that the transition might be of Kosterlitz-Thouless, XY-like character.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq= _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i – _i can be interpreted as clusters with an internal degree of freedom. The specific heat c and the susceptibility of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat c is an analytic function over the whole temperature range and the susceptibility shows a cusp at the transition temperatureT _c of the basic system.     

Metastability in the two-dimensional ising model

Metastability in the Ising model is studied in two ways. In a dynamical Monte Carlo model, metastable magnetization and lifetime are measured for various magnetic fields and low temperatures. Following up a proposed relation between analytic continuation of transfer matrix eigenvalues and metastability, transfer matrix eigenvalues are studied. We examine the extent to which these approaches agree. The Monte Carlo data also provide quantitative support for the critical droplet model for decay.     

Mean-field renormalization group with reaction field for diluted ising model

Summary A mean-field renormalization group method including the reaction field is applied to diluted Ising systems. Two-dimensional bond dilution and both two- and three-dimensional site dilution are considered. For low and intermediate dilution, the phase diagrams agree well with other predictions, while for large dilution (near the percolation threshold) pathologies may show up related to the choice of the reaction field at low temperature.

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Riassunto Un metodo di rinormalizzazione basato sul campo medio con correzioni di campo di reazione è applicato a modelli di Ising diluiti. Sone trattati sia il caso di legami diluiti in due dimensioni, che quello di siti diluiti in due e tre dimensioni. Per diluizioni non troppo elevate il diagramma delle fasi è in buon accordo con altre predizioni. Ad alte diluizioni (vicino alla soglia di percolazione) possono verificarsi patologie dovute all’inadeguatezza del campo di reazione a basse temperature.

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Резюме Группа перенормировки для среднего поля, включая поле взаимодействия, применяется к системам Изинга. Рассматриваются двумерное разбавление связи и двумерное и трехмерное разбавление узлов. Для слабого и среднего разбавления фазовые диаграммы хорошо согласуются с другими предсказаниями, однако для сильного раэбавления (вблизи порога перколяции) могут возникать патологии, связанные с выбором взаимодейстния при низкой температуре.