39 research outputs found
The Phase Diagram of an Anisotropic Potts Model
A study is made of an anisotropic Potts model in three dimensions where the
coupling depends on both the Potts state on each site but also the direction of
the bond between them using both analytical and numerical methods. The phase
diagram is mapped out for all values of the exchange interactions. Six distinct
phases are identified. Monte Carlo simulations have been used to obtain the
order parameter and the values for the energy and entropy in the ground state
and also the transition temperatures. Excellent agreement is found between the
simulated and analytic results. We find one region where there are two phase
transitions with the lines meeting in a triple point. The orbital ordering that
occurs in occurs as one of the ordered phases.Comment: 30 pages, 19 figures, one tabl
Tunneling and the Spectrum of the Potts Model
The three-dimensional, three-state Potts model is studied as a paradigm for
high temperature quantum chromodynamics. In a high statistics numerical
simulation using a Swendson-Wang algorithm, we study cubic lattices of
dimension as large as and measure correlation functions on long lattices
of dimension and . These correlations are
controlled by the spectrum of the transfer matrix. This spectrum is studied in
the vicinity of the phase transition. The analysis classifies the spectral
levels according to an underlying symmetry. Near the phase transition the
spectrum agrees nicely with a simple four-component hamiltonian model. In the
context of this model, we find that low temperature ordered-ordered interfaces
nearly always involve a disordered phase intermediate. We present a new
spectral method for determining the surface tension between phases.Comment: 26 pages plus 13 Postscript figures (Axis versions also provided),
UU-HEP-92/
Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions
The method of calculating the free energy and thermodynamic characteristics
of the classical n-vector three-dimensional (3D) magnetic model at the
microscopic level without any adjustable parameters is proposed. Mathematical
description is perfomed using the collective variables (CV) method in the
framework of the model approximation. The exponentially decreasing
function of the distance between the particles situated at the N sites of a
simple cubic lattice is used as the interaction potential. Explicit and
rigorous analytical expressions for entropy,internal energy, specific heat near
the phase transition point as functions of the temperature are obtained. The
dependence of the amplitudes of the thermodynamic characteristics of the system
for and on the microscopic parameters of the interaction
potential are studied for the cases and . The obtained
results provide the basis for accurate analysis of the critical behaviour in
three dimensions including the nonuniversal characteristics of the system.Comment: 25 pages, 5 figure
Screening Constitutional Isomers of C3H2O2 for Thermodynamic Properties Obtained from Systematic Electron Structure Calculations
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