61 research outputs found
Universal Amplitude Ratios for Constrained Critical Systems
The critical properties of systems under constraint differ from their ideal
counterparts through Fisher renormalization. The mathematical properties of
Fisher renormalization applied to critical exponents are well known: the
renormalized indices obey the same scaling relations as the ideal ones and the
transformations are involutions in the sense that re-renormalizing the critical
exponents of the constrained system delivers their original, ideal
counterparts. Here we examine Fisher renormalization of critical amplitudes and
show that, unlike for critical exponents, the associated transformations are
not involutions. However, for ratios and combinations of amplitudes which are
universal, Fisher renormalization is involutory.Comment: JSTAT published versio
Exact finite-size corrections for the spanning-tree model under different boundary conditions
We express the partition functions of the spanning tree on finite square
lattices under five different sets of boundary conditions (free, cylindrical,
toroidal, M\"obius strip, and Klein bottle) in terms of a principal partition
function with twisted boundary conditions. Based on these expressions, we
derive the exact asymptotic expansions of the logarithm of the partition
function for each case. We have also established several groups of identities
relating spanning-tree partition functions for the different boundary
conditions. We also explain an apparent discrepancy between logarithmic
correction terms in the free energy for a two dimensional spanning tree model
with periodic and free boundary conditions and conformal field theory
predictions. We have obtain corner free energy for the spanning tree under free
boundary conditions in full agreement with conformal field theory predictions.Comment: 13 pages. Expanded text with additional result
Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice
We solve the monomer-dimer problem on a non-bipartite lattice, the simple
quartic lattice with cylindrical boundary conditions, with a single monomer
residing on the boundary. Due to the non-bipartite nature of the lattice, the
well-known method of a Temperley bijection of solving single-monomer problems
cannot be used. In this paper we derive the solution by mapping the problem
onto one on close-packed dimers on a related lattice. Finite-size analysis of
the solution is carried out. We find from asymptotic expansions of the free
energy that the central charge in the logarithmic conformal field theory
assumes the value .Comment: 15 pages, 1 figure, submitted to Phy. Rev. E; v2: revised
Acknowledgment
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,
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