H. Gausterer

Surface tension and universality in the Ising model

We report on a new numerical computation of the surface tension between domains of opposite magnetisation in the Ising model in two and three dimensions. The method is quite general and can be applied to any statistical-mechanics model. It is based on a partition of the lattice into two halves, which are slowly driven from one magnetization state to the other. The free energy of the interface is the result of the difference between the total free energies of the homogeneous and of the mixed phases. We first test the method in the two-dimensional (ferromagnetic) Ising model by comparing with the Onsager solution. We then compare the results in three dimensions with previous Monte Carlo simulations of thermal equilibrium and of decays via nucleation. The three-dimensional results are also used in the computation of the universal amplitude combination that involves the correlation length and the surface tension. Near the critical temperature, the numerical results agree well with measurements performed in the laboratory.

Beyond the hopping expansion in the strongly coupled Schwinger model

Abstract It is tempting and seems to have become common to identify critical values of the hopping parameter κ with the radius of convergence of the expansion in κ. We argue that these two values differ in the strongly coupled lattice Schwinger model with Wilson fermions. We also determine the chiral condensate for all values of κ.

Strong coupling lattice Schwinger model on large spherelike lattices

Abstract The lattice regularized Schwinger model for one fermion flavor and in the strong coupling limit is studied through its equivalent representation as a restricted 8-vertex model. The Monte Carlo simulation on lattices with torus topology is handicapped by a severe non-ergodicity of the updating algorithm; introducing lattices with spherelike topology avoids this problem. We present 3 large scale study leading to the identification of a critical point with critical exponent ν = 1, in the universality class of the Ising model or, equivalently, the lattice model of free fermions.

Complex Langevin: A numerical method?

Abstract There are several problems in theoretical physics which are defined by complex valued weight functions e-S where S can be a complex action or classical Hamiltonian. Complex Langevin is one method to simulate integrals over such complex valued weights. The conditions under which the so called complex Langevin process can be related to the complex weight and correctly simulates such integrals are discussed.

Complex Langevin equations for fermion models

Abstract Based on spin coherent states, a method for constructing c-number fermionic path integrals is presented. Using stochastic quantization we demonstrate that good results are obtained for two specific models in d =2 by numerical solution of the associated complex Langevin equations.

Lee-Yang zeroes in the one flavour massive lattice Schwinger model

Abstract We study the partition function of the model formulated with Wilson fermions with only one species, both analytically and numerically. At strong coupling we construct the solution for lattice size up to 8×8, a polynomial in the hopping parameter up to O(κ128). At β>0 we evaluate the expectation value of the fermion determinant for complex values of κ. From the Lee-Yang zeroes we find support for the existence of a line of phase transitions from (β=0, κ⋍0.38) up to (β=∞, κ= 1 4 ) .

Breaking of chiral symmetry in compact QED in the strong coupling limit

Abstract We determine the value of the chiral condensate for compact QED at β =0. The finite size analysis is based on large volume expansion of chiral perturbation theory. It is therefore possible to determine the infinite volume, m =0 result on lattices much smaller than the Goldstone correlation length.

Operator oriented optimization of block spin transformations

Abstract We propose a generally applicable method to optimize block spin transformations. Working in the sector of even operators the renormalization transformation is adjusted such that the resulting renormalized trajectory is close to the trajectory of a simple few-parameter hamiltonian. The idea is tested within the d = 2 Ising model and leads to clear improvements in the determination of the critical exponents.

Two-dimensional model for strongly interacting matter at high particle density

Abstract For two-dimensional model theories, the global behaviour of the order parameter and the total charge at chemical potential μ ≠ 0 is studied with the use of complex Langevin equations.

STRONG COUPLING HADRON PROPAGATORS FOR MODIFIED FERMION ACTIONS

Abstract We discuss several possibilities to modify the fermionic action in lattice gauge theories and the effect on the meson and baryon propagators in strong coupling. There is an optimal value of r ≈ 0.25 but we find no improvement for the next nearest neighbour term and the straight two-link term.