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.     

Phase transition in one-dimensional lattice gauge theories

Considering one-dimensional nonminimally coupled lattice gauge theories, a class of nonlocal one-dimensional systems is presented which exhibits a phase transition. It is shown that the transition has a latent heat, and therefore is a first-order phase transition.     

Exact solution of the multiflavor gross-neveu model

The Bethe-ansatz solution is presented for the multiflavor model arising in the Polyakov-Wiegmann fermionization of the SU(2) principal chiral field, i.e. the O(4) σ model. The vacuum and excitations with finite energy and momentum are constructed. The assumption that massive particles of the σ model are in the vector representation of O(4) is not corroborated. The renormalization-group β function agrees with a one-charge solution in perturbation theory.     

Phase transition in the three-state Potts antiferromagnet on the diced lattice

We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically driven long-range order at low temperatures (including zero). We then present Monte Carlo simulations, using a cluster algorithm, of the 3-state and 4-state models. The 3-state model has a phase transition to the high-temperature disordered phase at v=e;{J}-1=-0.860 599+/-0.000 004 that appears to be in the universality class of the 3-state Potts ferromagnet. The 4-state model is disordered throughout the physical region, including at zero temperature.     

Phase transition in lattice surface systems with gonihedric action

We prove the existence of an ordered low-temperature phase in a model of soft-self-avoiding closed random surfaces on a cubic lattice by a suitable extension of Peierls contour method. The statistical weight of each surface configuration depends only on the mean extrinsic curvature and on an interaction term arising when two surfaces touch each other along some contour. The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version of the gonihedric string, which is an action for triangulated random surfaces.     

Phase transition in finite density and temperature lattice QCD

We investigate the behavior of the chiral condensate in lattice QCD at finite temperature and finite chemical potential. The study was done using two flavors of light quarks and with a series of β and ma at the lattice size 24×12²×6. The calculation was done in the Taylor expansion formalism. We are able to calculate the first and second order derivatives of <ψψ> in both isoscalar and isovector channels. With the first derivatives being small, we find that the second derivatives are sizable close to the phase transition and that the magnitude of ψψ decreases under the influence of finite chemical potential in both channels.     

States of non-zero density in the chiral invariant gross-neveu model

States describing a non-zero number density of massive particles are investigated in the SU(2) chiral-invariant Gross-Neveu model. It is found that for a fixed positive density, the lowest energy state is color ferromagnetic, with all color spins aligned. For asymptotically large densities, the total energy and density are calculated as functions of the Fermi momentum. These quantities tend toward their counterparts in a non-interacting theory, with logarithmic corrections typical of an asymptotically free system.     

Mott transition in ruby lattice Hubbard model

Mott transition in a ruby lattice with fermions described by the Hubbard model including on-site repulsive interaction is investigated by combining the cellular dynamical mean-field theory and the continuous-time quantum Monte Carlo algorithm. The effect of temperature and on-site repulsive interaction on the metallic–insulating phase transition in ruby lattice with fermions is discussed based on the density of states and double occupancy. In addition, the magnetic property of each phase is discussed by defining certain magnetic order parameters. Our results show that the antiferromagnetic metal is found at the low temperature and weak interaction region and the antiferromagnetic insulating phase is found at the low temperature and strong interaction region. The paramagnetic metal appears in whole on-site repulsive interaction region when the temperature is higher than a certain value and the paramagnetic insulator appears at the middle scale of temperature and on-site repulsive interaction.     

Phase transition in the generalized Ising-Kosterlitz-Thouless model

The features of the phase transition are considered in a model that is a combination of the Ising and Kosterlitz-Thouless models. It is shown that one or two successive phase transitions may occur in such a system, depending on the relation between parameters. An asymptotic formula is derived for the Ising-type phase transition temperature.     

Non-perturbative effects in the O(N) gross-neveu model

The construction of an ordered lagrangian for the O(N) Gross-Neveu model is presented. The procedure introduces a mass gap into the theory, prior to the development of perturbation theory. The results of the standard large N analysis of the theory, including mass generation, can then succesfully be produced. The renormalization of the ordered lagrangian at next to leading order is discussed in detail, and the large N corrections to the β-function are established.     

Phase transition of hard hexagons on a triangular lattice

Systems of hard hexagons on a triangular lattice are investigated. The orientation of the hexagons is kept fixed, while the size of the hexagons is varied. The existence of a phase transition is proved for all sizes by means of the Peierls'argument. The proof does not imply a phase transition in the continuous limit.Work supported by the U. S. Air Force under Contract No. F 44620-71-C-0013.     

Phase separation of the Potts model in the square lattice

When the two dimensional q-color Potts model in the square lattice is quenched at zero temperature with Glauber dynamics, the energy decreases in time following an Allen-Cahn power law, and the system converges to a phase with energy higher than the ground state energy after an arbitrary large time when q>4. At low but finite temperature, it cesses to obey the power-law regime and orders after a very long time, which increases with q, and before which it performs a domain growth process which tends to be slower as q increases. We briefly present and comment numerical results on the ordering at nonzero temperature.     

一簇金刚石晶格上S~4模型的相变

采用重整化群和累积展开的方法,研究了一簇金刚石晶格上S~4模型的相变,求得了系统的临界点.结果表明:当分支数m=2和m 12时,该系统只存在一个Gauss不动点K~*=b_2/2, u_2~*=0;当分支数3≤m≤12时,该系统不仅有Gauss不动点,还存在一个Wilson-Fisher不动点,并且后一个不动点对系统的临界特性产生决定性的影响.     

Phase transition in a lattice gas of hard spheres with second-neighbor exclusions on the simple cubic lattice

Using reflection positivity and the Peierls argument, we prove the existence of an ordered phase at sufficiently high activity for a lattice gas of hard spheres on the simple cubic lattice with first- and second-neighbor exclusions.     

Nuclear liquid-gas phase transition within the lattice gas model

We study the nuclear liquid-gas phase transition on the basis of a two-component lattice gas model. A Metropolis type of sampling method is used to generate microscopic states in the canonical ensemble. The effective equation of state and fragment mass distributions are evaluated in a wide range of temperatures and densities. A definition of the phase coexistence region appropriate for small systems is proposed. The caloric curve resulting from different types of freeze-out conditions are presented.     

Quantum phase transition in lattice model of unconventional superconductors

In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature (T). Finite-T counterpart of the present model was proposed previously with which SC phase transition at finite T was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.