14431113
Phase diagram of the chromatic polynomial on a torus
We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L = 5, 6, 7 for the square and triangular lattices. On the physical side, we obtain the exact phase diagrams for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases. © 2007 Elsevier B.V. All rights reserved.
119048676
Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices
We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on triangular and hexagonal lattices wrapped on a torus. We find the general form of the finite-size corrections to these quantities, as well as explicit formulae for the first coefficients of each expansion. We analyse the implications of these findings for the renormalization-group description of the model.
14803657
Dynamic critical behavior of the Swendsen-Wang algorithm: The two-dimensional three-state Potts model revisited
We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Sweden-Wang algorithm for the two-dimensional three-state Potts model. We find that the Li-Sokal bound (τint.δ⩾const×Cn) is almost but not quite sharp. The ratio τint.δ/Cn seems to diverge either as a small power (≈0.08) or as a logarithm.
59064818
On the non-ergodicity of the Swendsen–Wang–Kotecký algorithm on the kagomé lattice
We study the properties of the Wang–Swendsen–Kotecký cluster Monte Carlo algorithm for simulating the three-state kagome-lattice Potts antiferromagnet at zero temperature. We prove that this algorithm is not ergodic for symmetric subsets of the kagome lattice with fully periodic boundary conditions: given an initial configuration, not all configurations are accessible via Monte Carlo steps. The same conclusion holds for single-site dynamics.
118932027
Finite Size Analysis of the One-dimensional $q = \infty$ Clock Model
We analyze the finite size scaling of the $q$-state clock model in the $q \rightarrow \infty$ limit. The behaviors of the specific heat, Binder-Landau and U4 cumulants agree with the Borgs-Koteck\'y ans\"atz for first order phase transitions. However, we find that the leading correction to the position of the extremal points of these quantities is not universal. On the other hand, the finite size corrections to the mass gap behave like for second order phase transitions. In particular, the curves corresponding to different size approximations do not cross in the vicinity of the transition points. The feature is associated to the existence of a divergent correlation length and holds for a wider class of models.
18943104
Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model
A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.
122660242
Adiabatic regularization and particle creation for spin one-half fields
The extension of the adiabatic regularization method to spin-$1/2$ fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-$1/2$ fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.