Related papers: Zeros of the Potts Model Partition Function on Sie…
In this paper we consider the algorithmic problem of sampling from the Potts model and computing its partition function at low temperatures. Instead of directly working with spin configurations, we consider the equivalent problem of…
We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high and low…
We introduce the concept of quasi-metaparticles based on the theory of metaparticles, the zero modes of the metastring. We apply the concept of quasi-metaparticles to the problem of non-Fermi liquids and the properties of strange metals. In…
We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found…
The q-state ferromagnetic Potts model under a non-zero magnetic field coupled with the 0^th Potts state was investigated by an exact real-space renormalization group approach. The model was defined on a family of diamond hierarchical…
The microcanonical transfer matrix is used to study the distribution of Yang-Lee zeros of the $Q$-state Potts model in the complex magnetic-field ($x=e^{\beta h}$) plane for the first time. Finite size scaling suggests that at (and below)…
The method of counting loops for calculating the partition function of the Ising model on the two dimensional square lattice is extended to lacunary planar lattices, especially scale invariant fractal lattices, the Sierpi\'nsky carpets with…
All local bond-state densities are calculated for q-state Potts and clock models in three spatial dimensions, d=3. The calculations are done by an exact renormalization group on a hierarchical lattice, including the density recursion…
We present transfer matrices for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and M\"obius strips of the square, triangular, and honeycomb lattices of…
Thermopower and the Lorentz number for an edge-free (Corbino) graphene disk in the quantum Hall regime is calculated within the Landauer-B\"{u}ttiker formalism. We find, by varying the electrochemical potential, that amplitude of the…
We compute the semiclassical formulas for the partition functions obtained using two different Lagrangians: the Chern-Simons functional and the symplectic action functional.
We study partition functions and thermodynamic limits for the Ising model on three families of finite graphs converging to infinite self-similar graphs. They are provided by three well-known groups realized as automorphism groups of regular…
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field.…
We use the solutions of the noncommutative Wheeler-De Witt equation arising from a Kantowski-Sachs cosmological model to compute thermodynamic properties of the Schwarzschild black hole. We show that the noncommutativity in the momentum…
A new duality relation is derived for the Potts model in one dimension. It is shown that the partition function is self-dual with the nearest-neighbor interaction and the external field appearing as dual parameters. Zeroes of the partition…
Zeros of the moment of the partition function $[Z^n]_{\bm{J}}$ with respect to complex $n$ are investigated in the zero temperature limit $\beta \to \infty$, $n\to 0$ keeping $y=\beta n \approx O(1)$. We numerically investigate the zeros of…
We study the partition function per site of the integrable $Sp(2n)$ vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these functional relations in the thermodynamic…
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with…