Ising model with frustration,elasticity, and competing interactions

The Ising model on a compressible triangular lattice with axial next-nearestneighbor interactions is studied in the mean-field approximation. A representative phase diagram is generated, which exhibits first- and second-order phase transitions to commensurate modulated phases. The crossover point from first to second order transitions is calculated. The stability of the modulated phases is calculated analytically in a low-temperature approximation. These results are very different from the ANNNI model, which exhibits a second-order transition to a continuum of commensurate and incommensurate phases.     

Der Einfluß des elastischen Gitters auf den Orientierungsübergang von festem Ortho-Wasserstoff in Molekularfeldnäherung

We calculate the influence of the elastic lattice on the orientational order-disorder transition in fcc solid ortho-hydrogen. The angular momentaJ = 1 of the molecules are coupled by quadrupole-quadrupole interaction which we reduce within the space group Pa 3 to the Ising model approximation. Local mechanical equilibrium requires the lattice to adjust itself to the forces caused by the inhomogeneous fluctuations in the angular momentum configuration. Following Wagner [6] this results in a 4-angular-momentum interaction with long range and short range contributions depending on the one-phonon Green function of the lattice. We use a Debye phonon spectrum and the molecular field approximation in order to obtain numerical results. According to the first order nature of the phase transition we get a pressure drop at the critical pointT ^c of 9.7 bar. The experimental value is estimated to be 8 bar. Compared to the rigid lattice the phase transition on the elastic lattice is smoothed out by the short range contribution. This corresponds to a reduction of the discontinuity of the order parameter at the critical pointT ^c by about 13%. The phase transition will vanish completely if we increase the magnitude of the short range terms by a factor of three.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Exactly soluble planar Ising models on compressible lattices

Two planar Ising models on compressible lattices are considered. The elastic forces act in the horizontal direction only and between nearest-neighbors, but are otherwise arbitrary. The nearest-neighbor exchange interaction is taken as constant for two spins with the same column index and depending on separation for spins on the same row. In the first model (A) the transition remains continuous, and Fisher's theory of renormalized exponents applies; in the second model (B) the additional constraint that spins on a column move as a unit changes the transition to first order.     

Phase transition of the compressible ising lattice

It is shown that the presence of harmonic lattice vibrations in a spin-$\text{1}\text{2}$ Ising system leads, in the mean field approximation, to transitions of first or second order, according to whether the pressure lies below or above a critical value. The results are being discussed in relation to experiments on the order-disorder transition in NH₄Cl.     

Microcanonical relation between continuous and discrete spin models

A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of an Ising model defined on the same lattice suggests an approximate expression for the microcanonical density of states. Based on this approximation we conjecture that if a O(n) model with ferromagnetic interactions on a lattice has a phase transition, its critical energy density is equal to that of the n=1 case, i.e., an Ising system with the same interactions. The conjecture holds true in the case of long-range interactions. For nearest-neighbor interactions, numerical results are consistent with the conjecture for n=2 and n=3 in three dimensions. For n=2 in two dimensions (XY model) the conjecture yields a prediction for the critical energy of the Bere?inskij-Kosterlitz-Thouless transition, which would be equal to that of the two-dimensional Ising model. We discuss available numerical data in this respect.     

Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics

At zero temperature, based on the Ising model, the phase transition in a two-dimensional square lattice is studied using the generalized zero-temperature Glauber dynamics. Using Monte Carlo （MC） renormalization group methods, the static critical exponents and the dynamic exponent are studied; the type of phase transition is found to be of the first order.     

Phase structure of the FCC quartet Ising model

The phase structure of an Ising model with four-spin interactions defined on an FCC lattice is determined by Monte Carlo techniques. Our results show that this system undergoes a single, first order transition at the self-dual point. This resolves previous mutually contradictory conclusions which have been drawn about this model.     

The Phase Transition of the Quantum Ising Model is Sharp

An analysis is presented of the phase transition of the quantum Ising model with transverse field on the d-dimensional hypercubic lattice. It is shown that there is a unique sharp transition. The value of the critical point is calculated rigorously in one dimension. The first step is to express the quantum Ising model in terms of a (continuous) classical Ising model in d+1 dimensions. A so-called ‘random-parity’ representation is developed for the latter model, similar to the random-current representation for the classical Ising model on a discrete lattice. Certain differential inequalities are proved. Integration of these inequalities yields the sharpness of the phase transition, and also a number of other facts concerning the critical and near-critical behaviour of the model under study.     

Monte Carlo study of low/high spin transitions

We study the finite temperature property of a model on two dimensional square lattices with two Ising spins at each lattice site by Monte Carlo simulations. When those Ising spins at a lattice site are parallel the site is said to be in the high-spin state (HS), while when they are antiparallel the site is said to be in the low-spin state (LS). Throughout the study, the energy of HS is presumed to be higher than that of LS. Two Ising spins at each site are added to form a total spin, which interacts with its nearest neighbour total spins via spin-spin couplings. The spin-phonon coupling also is introduced via harmonic springs between nearest neighbour sites with spring constants and equilibrium distances depending on the spin states of the sites involved. In this system, we investigate the feature of transitions between LS and HS (to be called low/high spin transition (LHST)) by varying the temperature. As for the ferromagnetic interaction between total spins, the second order phase transition: pure HSmixed state of HS and LS is possible to occur in a pure spin system, as is expected from mean field calculations. The role of lattice distortions by the change of lattice spacings is shown to be essential for LHST: pure LS(pure)HS. In the model investigated, there appears an indication of the strong first order phase transition which reveals a conspicuous hysteresis.     

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.     

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.     

Ising deconfinement transition between Feshbach-resonant superfluids

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.     

Geometrical aspects of the Z-invariant Ising model

We discuss a geometrical interpretation of the Z-invariant Ising model in terms of isoradial embeddings of planar lattices. The Z-invariant Ising model can be defined on an arbitrary planar lattice if and only if certain paths on the lattice edges do not intersect each other more than once or self-intersect. This topological constraint is equivalent to the existence of isoradial embeddings of the lattice. Such embeddings are characterized by angles which can be related to the model coupling constants in the spirit of Baxter's geometrical solution. The Ising model on isoradial embeddings studied recently by several authors in the context of discrete holomorphy corresponds to the critical point of this particular Z-invariant Ising model.     

Phase diagram of magnetic polymers

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in a good solvent. These polymers are modeled as self-avoiding walks on a cubic lattice, and the ferromagnetic interaction between the spins carried by the monomers is short-ranged in space. At low temperature, these polymers undergo a magnetic induced first order collapse transition, that we study at the mean field level. Contrasting with an ordinary point, there is a strong jump in the polymer density, as well as in its magnetization. In the presence of a magnetic field, the collapse temperature increases, while the discontinuities decrease. Beyond a multicritical point, the transition becomes second order and -like. Monte Carlo simulations for the Ising case are in qualitative agreement with these results. Received 11 February 1999     

Peierls-like transition induced by frustration in a two-dimensional antiferromagnet

We show that the introduction of frustration into the spin- 1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest-neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for Li(2)VOSiO(4), the first realization of that model, will be discussed.     

Phase diagrams of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice

The ground-state and finite-temperature behavior of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice is investigated within the framework of two rigorous methods: the decoration-iteration transformation and exact recursion relations. The model under consideration describes a hybrid classical-quantum system consisting of the Ising and Heisenberg spins, which interact among themselves either through the Ising or XXZ Heisenberg nearest-neighbor interaction. Both sublattice magnetizations of the Ising and Heisenberg spins are exactly calculated with the aim to examine phase diagrams, thermal variations of the total and sublattice magnetizations. The finite-temperature phase diagrams form continuous (second-order) phase transition lines only, which exhibit a small reentrant region if the diamond-like decorated Bethe lattice with a sufficiently high coordination number is considered.     

Lattice gas model for monolayer of amphipatic molecules

Using the molecular-field approximation for the lattice gas model in terms of a spin-one Ising model, we construct phase diagrams and show when the transition could be of first or second order. Possible relevance to the theoritical models of phase transitions in monolayers of amphipatic molecules is also discussed.     

Phase transitions in cold and warm dense matter

We consider the phase transitions, in dense matter, from nuclei to bubbles and from bubbles to uniform matter. A simplified version of the compressible liquid-drop model allows us to discuss analytically the densities at which the free energies of the different phases are equal, and the density discontinuities of the phases in equilibrium. A reasonable agreement with detailed numerical calculations is obtained only if the compressibility of the matter inside nuclei, and particularly outside bubbles, is taken into account. The dependence of the bubbles-uniform matter transition on the various elements of the Coulomb energy is discussed in detail: the transition is actually a first-order one, but it becomes of second order if the lattice Coulomb energy is turned off.The insight into the effect on the transition of the ratio of surface-plus-Coulomb energy to compression modulus allows us to understand the dependence of the transition densities on temperature and on the microscopic model employed.     

Percolation transition in an irreversible-surface reaction model

Monte Carlo simulation studies of percolation transition in a surface reaction model describing the oxidation of carbon mono-oxide on a catalytic surface are presented. The percolation transition for adsorbed oxygen atoms occurs below the poisoning transition where carbon mono-oxide completely covers the surface of the catalyst and takes place for an oxygen coverage of about 0.525 which is close to the percolation transition in an Ising lattice gas with nearest-neighbor attractive interactions. In several respects the oxygen clusters near the percolation threshold resemble those of the Ising lattice gas near its critical point.