K. Pinn

Computing the roughening transition of Ising and solid-on-solid models by BCSOS model matching

We study the roughening transition of the dual of the two-dimensional (2D) XY model, of the discrete Gaussian model, of the absolute value solid-on-solid model and of the interface in an Ising model on a three-dimensional (3D) simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body-centred solid-on-solid (BCSOS) model. Our estimates for the critical couplings are , and for the XY model, the discrete Gaussian model and the absolute value solid-on-solid model, respectively. For the inverse roughening temperature of the Ising interface we find . To the best of our knowledge, these are the most precise estimates for these parameters published so far.

Stochastic cluster algorithms for discrete gaussian (SOS) models

Abstract We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z . Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm.

Rough interfaces beyond the Gaussian approximation

We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).

Canonical demon Monte Carlo renormalization group

Abstract We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. In contrast to the Microcanonical Renormalization Group invented by Creutz et al. our method does not suffer from systematical errors stemming from a simultaneous use of two different ensembles. We present numerical results for the O (3) nonlinear σ-model.

Iterating block spin transformations of the O(3) nonlinear sigma model.

We study the iteration of block spin transformations in the O(3) symmetric nonlinear {sigma} model on a two-dimensional square lattice with the help of the Monte Carlo method. In contrast with the classical Monte Carlo renormalization group approach, we {ital do} attempt to explicitly compute the block spin effective actions. Using two different methods for the determination of effective couplings, we study the renormalization group flow for various parametrization and truncation schemes. The largest ansatz for the effective action contains thirteen coupling constants. Actions on the renormalized trajectory should describe theories with no lattice artifacts, even at a small correlation length. However, tests with the step scaling function of L{umlt u}scher, Weisz, and Wolff reveal that our truncated effective actions show sizable scaling violations indicating that the {ital Ans{umlt a}tze} are still too small. {copyright} {ital 1996 The American Physical Society.}

Monte Carlo simulation of 2D quantum gravity as open dynamically triangulate random surfaces

We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to fluctuate. The algorithm works in the presence of matter fields. We here present results for the pure gravity case. The algorithm reproduces the theoretical expectations.

Renormalization group flow of a hierarchical Sine-Gordon model by partial differential equations

We use a renormalization group differential equation to rigorously control the renormalization group flow in a hierarchical lattice Sine-Gordon field theory in the Kosterlitz-Thouless phase.

A Monte Carlo procedure for hamiltonians with small nonlocal correction terms

Abstract Lattice field theories are considered whose hamiltonians contain small nonlocal correction terms. It is proposed to do simulations for an auxiliary polymer system with field-dependent activities. If a nonlocal correction term to the hamiltonian is small, it need be evaluated only rarely.

New estimates on various critical/universal quantities of the 3D Ising model

We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude σ0 in the critical law σ = σ0τμ, and for the universal combination R− = σξ2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+A−, together with the exponent α, the nonsingular background of energy and specific heat at criticality, together with the exponent ν. There are also results for the universal combination fsξ3, where fs is the singular part of the free energy. Details can be found in [1] (interface) and [2] (bulk).

The sine Gordon model: perturbation theory and cluster Monte Carlo

We study the expansion of the surface thickness in the 2-dimensional lattice sine Gordon model in powers of the fugacity z. Using the expansion to order z2, we derive lines of constant physics in the rough phase. We describe and test a VMR cluster algorithm for the Monte Carlo simulation of the model. The algorithm shows nearly no critical slowing down. We apply the algorithm in a comparison of our perturbative results with Monte Carlo data.