An alternative order parameter for the 4-state Potts model

We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A: Math. Gen. \textbf{20}, L549 (1987)] in the study of the Z(5) model. We have estimated the global persistence exponent $\theta_g$ by following the time evolution of the probability $P(t)$ that the considered order parameter does not change its sign up to time $t$. We have also obtained the critical exponents $\theta$, $z$, $\nu$, and $\beta$ using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.Comment: 6 pages, 6 figure

Two-dimensional lattice polymers: adaptive windows simulations

We report a numerical study of self-avoiding polymers on the square lattice, including an attractive potential between nonconsecutive monomers. Using Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of states for chains of up to N=300 monomers and associated thermodynamic quantities. The method enables one to simulate accurately the low-temperature regime, which is virtually inaccessible using traditional methods. Instead of defining fixed energy windows, as in usual WLS, this method uses windows with boundaries that depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor $f$ is reduced, we eliminate border effects that arise in simulations using fixed windows.Comment: 8 pages, 5 figure

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.

A statistical mechanical study of thermodynamic properties of solid sodium under pressure based on an effective interionic potential

Basing on the Schiff effective interionic potential that has an oscillatory character and the correlative method of unsymmetrized self-consistent field (CUSF) that enables one to take into account the strong anharmonicity of the crystal lattice vibrations, we have calculated a complete set of equilibrium thermodynamic properties of solid sodium as functions of pressure and temperature: the lattice parameter, the elastic moduli, the thermal expansion coefficient, the Grüneisen parameter and the isochoric and isobaric heat capacities. Our results are compared with available experimental data. We also discuss the thermodynamic stability of the BCC lattice, the mechanism of its loss and its change under pressure

A statistical mechanical study of thermodynamic properties of solid sodium under pressure based on an effective interionic potential

Basing on the Schiff effective interionic potential that has an oscillatory character and the correlative method of unsymmetrized self-consistent field (CUSF) that enables one to take into account the strong anharmonicity of the crystal lattice vibrations, we have calculated a complete set of equilibrium thermodynamic properties of solid sodium as functions of pressure and temperature: the lattice parameter, the elastic moduli, the thermal expansion coefficient, the Grüneisen parameter and the isochoric and isobaric heat capacities. Our results are compared with available experimental data. We also discuss the thermodynamic stability of the BCC lattice, the mechanism of its loss and its change under pressure

On thermodynamic properties of crystals in the metastable region

The possibility of superheating crystals has been firmly established but experimental investigations of their metastable states present great difficulties. We have undertaken a theoretical study of their thermodynamic properties near the limit of stability. Using the correlative method of unsymmetrized self-consistent field, we have explored the properties of Van der Waals crystals with the face-centered cubic lattice. The exponents governing their peculiarities in the vicinity of the unstable point have been evaluated and discussed. © 1994

Statistical thermodynamics of bosons in one- and two-level quantum wells

This paper deals with the thermodynamics of bosons in a three-dimensional square potential of a single- or two-level isolated quantum well. On evaluating the main thermodynamic properties, we find certain expected features: Bose condensation and also a phase transition as a second level is introduced. Its strength depends on the number of particles in the well. The question of energy and entropy additivity and the behaviour of the chemical potential is also discussed

Isotherms, thermodynamic properties and stability of the FCC phase of the C60 fullerite: A theoretical study

We are pursuing statistical-mechanical investigations of thermodynamic properties of the high-temperature modification of the C60 fullerite taking into account the intramolecular degrees of freedom and the strong anharmonicity of lattice vibrations. In our theoretical calculations we employed the correlative method of an unsymmetrized self-consistent field for strongly anharmonic crystals using the available experimental information about the vibrational spectrum of this molecule. The Girifalco potential and the Yakub approximation are used. In the present work we have calculated isotherms of this fullerite and a complete set of its equilibrium properties, including the components of the elastic tensors. Each isotherm has two branches V1(P) < V2(P), which coalesce at some (minimal) pressure that depends on the temperature. At the left branch, BT(P, V1) > 0, while at the right one, BT(P, V2) < 0; the latter represents the absolute instability of the states V2(P). We have also investigated the thermodynamic stability of this fullerite and the mechanism of loss of stability depending on the temperature. Our results for thermal and elastic properties are in good agreement with experimental data available at low pressures and temperatures. © 1997 Elsevier Science Ltd