Spin models in complex magnetic fields: a hard sign problem

¹ ETH Zürich, Institute for Theoretical Physics, Wolfgang-Pauli-Str. 27, CH-8093 Zürich, Switzerland
² CERN, Theory Division, CH-1211 Geneva 23, Switzerland
³ University of Helsinki, Department of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland

^* Speaker, e-mail: tobias.rindlisbacher@helsinki.fi

Published online: 26 March 2018

Abstract

Coupling spin models to complex external fields can give rise to interesting phenomena like zeroes of the partition function (Lee-Yang zeroes, edge singularities) or oscillating propagators. Unfortunately, it usually also leads to a severe sign problem that can be overcome only in special cases; if the partition function has zeroes, the sign problem is even representation-independent at these points. In this study, we couple the N-state Potts model in different ways to a complex external magnetic field and discuss the above mentioned phenomena and their relations based on analytic calculations (1D) and results obtained using a modified cluster algorithm (general D) that in many cases either cures or at least drastically reduces the sign-problem induced by the complex external field.