1,080 research outputs found
Exact phase diagrams for an Ising model on a two-layer Bethe lattice
Using an iteration technique, we obtain exact expressions for the free energy
and the magnetization of an Ising model on a two - layer Bethe lattice with
intralayer coupling constants J1 and J2 for the first and the second layer,
respectively, and interlayer coupling constant J3 between the two layers; the
Ising spins also couple with external magnetic fields, which are different in
the two layers. We obtain exact phase diagrams for the system.Comment: 24 pages, 2 figures. To be published in Phys. Rev. E 59, Issue 6,
199
The 6-vertex model of hydrogen-bonded crystals with bond defects
It is shown that the percolation model of hydrogen-bonded crystals, which is
a 6-vertex model with bond defects, is completely equivalent with an 8-vertex
model in an external electric field. Using this equivalence we solve exactly a
particular 6-vertex model with bond defects. The general solution for the
Bethe-like lattice is also analyzed.Comment: 13 pages, 6 figures; added references for section
Finite-size corrections for logarithmic representations in critical dense polymers
We study (analytic) finite-size corrections in the dense polymer model on the
strip by perturbing the critical Hamiltonian with irrelevant operators
belonging to the tower of the identity. We generalize the perturbation
expansion to include Jordan cells, and examine whether the finite-size
corrections are sensitive to the properties of indecomposable representations
appearing in the conformal spectrum, in particular their indecomposability
parameters. We find, at first order, that the corrections do not depend on
these parameters nor even on the presence of Jordan cells. Though the
corrections themselves are not universal, the ratios are universal and
correctly reproduced by the conformal perturbative approach, to first order.Comment: 5 pages, published versio
Most vital segment barriers
We study continuous analogues of "vitality" for discrete network flows/paths,
and consider problems related to placing segment barriers that have highest
impact on a flow/path in a polygonal domain. This extends the graph-theoretic
notion of "most vital arcs" for flows/paths to geometric environments. We give
hardness results and efficient algorithms for various versions of the problem,
(almost) completely separating hard and polynomially-solvable cases
Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus
For the free models of statistical mechanics on torus, exact asymptotic
expansions of the free energy, the internal energy and the specific heat in the
vicinity of the critical point are found. It is shown that there is direct
relation between the terms of the expansion and the Kronecker's double series.
The latter can be expressed in terms of the elliptic theta-functions in all
orders of the asymptotic expansion.Comment: REVTeX, 22 pages, this is expanded version which includes exact
asymptotic expansions of the free energy, the internal energy and the
specific hea
Exact Ampitude Ratio and Finite-Size Corrections for the M x N Square Lattice Ising Model The :
Let f, U and C represent, respectively, the free energy, the internal energy
and the specific heat of the critical Ising model on the square M x N lattice
with periodic boundary conditions. We find that N f and U are well-defined odd
function of 1/N. We also find that ratios of subdominant (N^(-2 i - 1))
finite-size corrections amplitudes for the internal energy and the specific
heat are constant. The free energy and the internal energy at the critical
point are calculated asymtotically up to N^(-5) order, and the specific heat up
to N^(-3) order.Comment: 18 pages, 4 figures, to be published in Phys. Rev. E 65, 1 February
200
Exact correlation functions of Bethe lattice spin models in external fields
We develop a transfer matrix method to compute exactly the spin-spin
correlation functions of Bethe lattice spin models in the external magnetic
field h and for any temperature T. We first compute the correlation function
for the most general spin - S Ising model, which contains all possible
single-ion and nearest-neighbor pair interactions. This general spin - S Ising
model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths
(BEG) model as special cases. From the spin-spin correlation functions, we
obtain functions of correlation length for the simple Ising model and BEG
model, which show interesting scaling and divergent behavior as T approaches
the critical temperature. Our method to compute exact spin-spin correlation
functions may be applied to other Ising-type models on Bethe and Bethe-like
lattices.Comment: 19 page
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