RANDOM-LATTICE MODELS AND SIMULATION ALGORITHMS FOR THE PHASE-EQUILIBRIA IN 2-DIMENSIONAL CONDENSED SYSTEMS OF PARTICLES WITH COUPLED INTERNAL AND TRANSLATIONAL DEGREES OF FREEDOM
M. Nielsen et al., RANDOM-LATTICE MODELS AND SIMULATION ALGORITHMS FOR THE PHASE-EQUILIBRIA IN 2-DIMENSIONAL CONDENSED SYSTEMS OF PARTICLES WITH COUPLED INTERNAL AND TRANSLATIONAL DEGREES OF FREEDOM, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(6), 1996, pp. 6889-6905
In this work we concentrate on phase equilibria in two-dimensional con
densed systems of particles where both translational and internal degr
ees of freedom are present and coupled through microscopic interaction
s, with a focus on the manner of the macroscopic coupling between the
two types of degrees of freedom. First, an unconventional description
of the translational degrees of freedom is developed, in which the ran
domly varying spatial connectivity of the particles is represented by
a random lattice whose dynamic structure is given by triangulating the
spatial configurations. Based on this random-lattice description, a s
eries of three statistical-mechanical models are then constructed. All
of the three models are in essence spin-1/2 Ising models where the sp
ins, representing internal degrees of freedom, are associated with har
d-disk particles and nearest-neighbor particles interact through spin-
spin interactions that may have spatial dependence. The fluctuating nu
mber of nearest neighbors and the possible spatial dependence of the s
pin-spin interactions couple microscopically the spin degrees of freed
om to the translational degrees of freedom. The first model (I) is a r
andom-lattice Ising model with conventional nearest-neighbor spin-spin
interactions. The second model (II) is an extension of this model to
include a spatial dependence of the nearest-neighbor spin-spin interac
tions. The third model (III) is a modification of the second model tha
t accounts for spin states with different internal degeneracy. Monte C
arlo simulation techniques, including both a special algorithm for the
random-lattice description and histogram and finite-size scaling anal
ysis, are used to investigate the phase behavior of all three models.
It is shown that the order-disorder spin transition in model I is deco
upled from a first-order singularity-lattice melting-associated with t
he translational degrees of freedom and remains critical and falls in
the universality class of the standard two-dimensional Ising model on
regular lattices. Model II is shown to exhibit a phase diagram that ha
s a region where the spin degrees of freedom are slaved by the transla
tional degrees of freedom and develop a first-order singularity in the
order-disorder transition that accompanies the lattice-melting transi
tion. The internal degeneracy of the spin states in model III implies
that the spin order-disorder singularity can be of first order through
out the phase diagram. It is found that this first-order singularity c
an be either coupled to or decoupled from the lattice-melting singular
ity, depending on the strength of the microscopic coupling. The calcul
ated phase diagram and the associated thermodynamic transitional prope
rties for model III are discussed in relation to experiments on planar
bilayers of lipid-chain molecules whose properties are determined by
a subtle coupling between the translational variables and the intracha
in conformational states.