Two- and three-spin triangular ising model: Variational approximations

The implications of the known hard-hexagon lattice gas results for the triangular Ising model with both pair and triplet interactions are pointed out. Employing an appropriate generalization of the variational method of Baxter we determine, using the lowest-order approximation, the phase boundaries for this model when the pair interactions are ferromagnetic. Higher approximations are presented for the case of pure triplet interactions and the resulting phase diagrams are in excellent agreement with all exactly known results.     

Ising models with two- and three-spin interactions: Mean field equation of state

The Ising model with pair and triplet interactions on the triangular lattice is solved in the mean-field approximation. With a sufficiently strong triplet interaction two first-order transitions take place at low temperature, and at intermediate temperatures one transition, terminating in a critical point. For J₂ > 0.75J₃ only the latter transition remains.     

Ising models with two-and three-spin interactions

Three Ising models with two- and three-spin interactions are shown to be exactly solvable. Their critical behaviour: non-universal dependence of the critical exponents on the interaction parameters in one case, absence of finite critical temperature in the second case and logarithmic singularity of the specific heat in the third one, is different from the recent conjecture that such models belong to the Baxter-Wu universality class.     

Ordering and phase transitions in ising systems with competing short range and dipolar interactions

As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ ²/a ³. ForJa ³/µ ²Ja ³/µ ²<0.1270 the ground state consists of ferromagnetic rows (in spin direction) arranged antiferromagnetically in the plane perpendicular to it. AtJa ³/µ ²=0.1279 the structure changes to a layered antiferromagnetic structure with a twocomponent order parameter, while forJa ³/µ ²>0.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa ³/µ ² where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero. The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa ³/µ ² of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.     

On the critical behavior of the Ising model with mixed two- and three-spin interactions

A study is made of a two-dimensional Ising model with staggered three-spin interactions in one direction and two-spin interactions in the other. The phase diagram of the model and its critical behavior are explored by conventional finite-size scaling and by exploiting relations between mass gap amplitudes and critical exponents predicted by conformal invariance. The model is found to exhibit a line of continuously varying critical exponents, which bifurcates into two Ising critical lines. This similarity of the model with the Ashkin-Teller model leads to a conjecture for the exact critical indices along the nonuniversal critical curve. Earlier contradictions about the universality class of the uniform (isotropic) case of the model are clarified.     

Frustrations and phase transitions in the three-vertex Potts model with next-nearest-neighbor interactions on a triangular lattice

Phase transitions in two-dimensional arrays described by the three-vertex Potts model involving the interactions between magnetic moments located at the nearest-neighbor and next-nearest-neighbor sites of a triangular lattice are studied using the Monte Carlo method. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r = J ₂/J ₁ is chosen within the 0–1 range. The analysis of the low temperature behavior of the entropy and density of states in the system, as well as of the fourth-order Binder cumulants, shows that in the range 0 ≤ r < 0.2, this model exhibits a first-order phase transition, whereas at r ≥ 0.2, frustrations arise in such a system.     

Inverse problem of inhomogeneous ising models with many-spin interactions

We study the inverse problem of inhomogeneous Ising lattices with a general spin which consists in finding the external potential required to produce a given profile of equilibrium single-site distributions. In particular, we extend a previously developed two-step procedure for simplifying the inverse problem to the case of many-spin interactions. The general procedure is applied to a special chain withh-spin interactions for which the inverse problem is, in principle and forh=2, 3, 4 also in practice, solvable exactly. Direct correlation functions of the proposed model have only short-range support.     

Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.     

Fourier transform double-resonance NMR on two- and three-spin systems

The flip angle dependence of the line intensities in gated double-resonance FT NMR experiments on the strongly coupled spin systems 2,3-dibromothiophene, 1,2,3-trichlorobenzene, vinyl acetate, and 2,3-dibromopropionic acid is shown to follow the theory of Shäublin, Höhener, and Ernst. A general method for analysis of the flip-angle-dependent intensities in terms of spin level population differences is described, and it is demonstrated that the variation of line intensities with flip angle is sensitive to the relative signs of spin-spin couplings and to the mechanism of spin relaxation.     

Second-order phase transitions under pressure in polycrystalline compounds and rocks

Bulletin of the Russian Academy of Sciences: Physics - The dependence of thermal conductivity in mono-and polycrystalline tellurium and rocks at hydrostatic pressures of up to 400 MPa in the...     

Second-order phase transitions and Ehrenfest equation for strained solids

The equations describing the second-order phase transitions at the hydrostatic and non-hydrostatic pressures are considered. It is shown that the proportionality coefficient between an “effective” volume and the true one V^??=?AV is inversely proportional to the compressibility of the solid at a uniaxial pressure and has a jump at the second-order phase transition. In the case of the non-hydrostatic pressure the “effective” volume of the solid is not a continuous function of temperature and has a jump at the phase transition as well. The Ehrenfest equation is generalized to the solids with an arbitrary homogeneous elastic deformation accompanied by change of the solid volume, in particular, to the solid strained by the uniaxial, biaxial or triaxial pressure. It is shown that the sum of the derivatives of the phase transition temperature with respect to uniaxial pressures applied along axes a, b, c does not coincide with the derivative of the phase transition temperature with respect to the hydrostatic pressure.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

One-dimensional chiral models with first-order phase transitions

A family of one-dimensional classical chiral spin models with groupG=U(N) orSU(N) is introduced, having complex nearest-neighbor interaction. TheseG×G invariant systems have self-adjoint positive transfer matrices and satisfy reflection positivity. In the case ofG=U(N), forN=1, 2, 3, sequences of first-order phase transitions are shown to occur.     

Modulated phase of an ising system with competing interactions on a Cayley tree

A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered on a Cayley tree. The phase diagram contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. The variation of the wavevector with temperature in the modulated phase is studied in detail, it shows narrow commensurate steps between incommensurate regions (incomplete devil's staircase). The behaviour of the coherence length near the different transitions is also analyzed.     

Ground state of a spin system with two- and four-spin exchange interactions on the triangular lattice

We study a spin system with both two- and four-spin exchange interactions on the triangular lattice as a possible model for the nuclear magnetism of solid ³He layers adsorbed on grafoil. The ground state is analyzed by the use of the mean-field approximation. It is shown that the four-sublattice state is favored by introduction of the fourspin exchange interaction. A possible phase transition at a finite temperature into a phase with the scalar chirality is predicted. Application of a magnetic field is shown to cause a variety of phase transitions.     

Critical line of the triangular potts model with two- and three-site interactions: An alternate derivation

A double star-triangle relation which is a generalization of the usual single star-triangle relation is introduced. Together with a duality transformation it is possible to rederive the critical line of the Potts model with two- and three-site interactions on alternate triangles.     

Magnetic phase transitions in amorphous systems with competing exchange interactions

A method is proposed for analyzing magnetic phase transitions within the Ising model under the conditions of competing direct and indirect exchange interactions. It is demonstrated that the competition of exchange interactions leads to a reentrant phase transition between the ferromagnet and spin glass near the percolation threshold below the Curie temperature.