We study the global phase diagram of infinite-range Blume-Emery-Griffiths model both in canonical and microcanonical ensembles. The shows first-order continuous transition lines separated by a tricritical point. find that below point, when is first order, diagrams two ensembles disagree. In this region ensemble exhibits energy ranges with negative specific heat temperature jumps at energies. These results can be extended to weakly decaying nonintegrable interactions.

A simple model of a driven diffusive system which exhibits spontaneous symmetry breaking in one dimension is introduced. The has short range interactions and unbounded noise. It characterized by an asymmetric exclusion process two types charges moving opposite directions on open chain. studied mean field Monte Carlo methods. Exact solutions can be found restricted region its parameter space. physical picture for the mechanism presented.

We study a model for the denaturation transition of DNA in which molecules are considered as composed sequence alternating bound segments and denaturated loops. take into account excluded-volume interactions between loops rest chain by exploiting recent results on scaling properties polymer networks arbitrary topology. The phase is found to be first order d=2 dimensions above, agreement with experiments at variance previous theoretical results, only within were taken account. Our agree...

Certain phase transitions which involve an increase of the unit cell in one or more directions, are described by $n\ensuremath{\ge}4$-component vector models. According to universality, critical behavior a system should depend only upon small number parameters such as dimensionality space, components order parameter, and symmetry Hamiltonian. We suggest that it would be great interest study these $n\ensuremath{\ge}4$ systems experimentally, examine effect parameter anisotropy on behavior....

Existing theories for commensurate-incommensurate transitions in one-dimensionally-modulated systems show that these are continuous and associated with domainwall formation. We consider the effect of domain-wall crossing two-dimensionally modulated hexagonal symmetry such as rare-gas layers adsorbed on graphite layered compound $2H$-Ta${\mathrm{Se}}_{2}$. if transition is continuous, broken incommensurate phase, while first order can be maintained phase. The experimental consequences this...

An Ising model with spin $S=1$ at each lattice point which exhibits multiple tricritical points is presented. This a generalization of the Blume-Emery-Griffiths was used for describing in ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures. The solved molecular-field approximation. It found that its thermodynamic behavior near qualitative agreement ternary fluids their points.

The first-order nature of the antiferromagnetic transitions in Cr, Eu, U${\mathrm{O}}_{2}$, and MnO can be explained by noting that corresponding Landau-Ginzburg-Wilson Hamiltonians possess no stable fixed points $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions. We predict all fcc type-I ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{m}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$), type-II, type-III...

We use the symmetry arguments of Laudau and Lifshitz, described in preceding papers, to derive Landau-Ginzburg-Wilson Hamiltonians corresponding several antiferromagnetic systems. The phase transitions associated with these models are then studied using exact renormalization-group technique $d=4\ensuremath{-}\ensuremath{\epsilon}$ dimensions. find that fcc type-III antiferromagnets...

The thermodynamic and dynamical properties of an Ising model with both short range long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that relaxation time thermodynamically unstable states diverges logarithmically system size. This in contrast case where this finite. Moreover, at sufficiently low energies, gaps magnetization interval may develop to which no microscopic configuration corresponds. As a result, local dynamics cannot move across...

In the preceding paper, we derived $n\ensuremath{\ge}4$-component Landau-Ginzburg-Wilson Hamiltonians describing phase transitions in certain physical systems. Here, use Wilson's $\ensuremath{\epsilon}$ expansion to study associated with these Hamiltonians. Although $n=4$ systems Tb${\mathrm{Au}}_{2}$, Dy${\mathrm{C}}_{2}$, and Nb${\mathrm{O}}_{2}$ have different symmetries, they are predicted same critical exponents. Similarly, although $n=6$ Tb${\mathrm{D}}_{2}$, Nd,...

It is shown by a calculation analogous to that carried out Wallace and Zia for the pure Ising model lower critical dimension of in random field 3 not 2 as suggested domain energy arguments. Further, roughening transition be 5 compared model.

A driven diffusive model of three types particles that exhibits phase separation on a ring is introduced. The dynamics local and comprises nearest-neighbor exchanges conserve each the species. For case in which densities are equal, it shown obeys detailed balance. Hamiltonian governing steady state distribution this given found to have long range asymmetric interactions. partition sum bounds some correlation functions calculated analytically demonstrating separation.

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It suggested that related to size dependence steady-state currents domains system. quantitative conjectured using a correspondence made between diffusive models and zero-range processes. The verified all cases where analytical results are available, predictions other provided.

The late time evolution and structure of 2D Rayleigh-Taylor Richtmyer-Meshkov bubble fronts is calculated, using a new statistical merger model based on the potential flow equations. dynamics are shown to reach scale invariant reigme. It found that front reaches constant acceleration, growing as 0.05${\mathit{gt}}^{2}$, while grows ${\mathit{at}}^{0.4}$ where depends initial perturbation. results in good agreement with experiments simulations.

We present a lattice-gas model of ternary fluid mixtures. Within the mean-field approximation, we study nonsymmetric tricritical point in this model. compare our results to experimental observations on system ethanol-water-carbon-dioxide. In course work, have studied Landau theory describing neighborhood fourth-order critical point. Also, noted that indicates existence spin-1 Blume, Emery, and Griffiths, corresponding $K<0$, $J+K>0$.

It is pointed out that certain phase transitions which involve a doubling of the unit cell are described by $n$-component vector models with $n>~4$. In particular, it noted structural transition in Nb${\mathrm{O}}_{2}$ an $n=4$ component model some tetragonal anisotropy. The critical behavior this studied to order ${\ensuremath{\epsilon}}^{2}$, exact renormalization group $d=4\ensuremath{-}\ensuremath{\epsilon}$ dimensions. found determined new, tetragonal, fixed point.

Various physical systems with Hamiltonians of cubic and lower symmetry are predicted classically to exhibit second-order phase transitions but known yield first-order within the renormalization-group approach either (a) because no appropriate "stable" fixed point exists, or (b) stable is not physically accessible. [MnO seems be an example (a).] This situation discussed under circumstances where imposition a further symmetry-beaking field, $g\ensuremath{\gg}1$, restores continuous transition....

The (${H}_{x}, {H}_{y}, {H}_{z}$) phase diagram of a cubic ferromagnet with three easy axes, in field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}=({H}_{x}, {H}_{z})$, is studied by mean-field, scaling, and renormalization-group theories. For $T&lt;{T}_{c}(H=0)$ $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}[111]$ there transition at fields $\ifmmode\pm\else\textpm\fi{}{H}_{0}(T)$, described the three-component Potts model. By varying...

We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions that exhibits a mixed-order transition, namely phase transition in which the order parameter is discontinuous as first transitions while correlation length diverges second transitions. Such are known to appear diverse classes of models seemingly unrelated. The we present serves link between two exhibit one dimension, namely, spin coupling constant decays inverse distance squared depinning...

II Aprt/ /994, a(.(.epled il? fil?a/ foi-ni 5./u/).

A driven system of three species particles diffusing on a ring is studied in detail. The dynamics local and conserves the densities. simple argument suggesting that model should phase separate break translational symmetry given. We show for special case where densities are equal obeys detailed balance, steady-state distribution governed by Hamiltonian with asymmetric long-range interactions. This provides an explicit demonstration mechanism breaking ergodicity one dimension. steady state...