On the Segregation Phenomenon in Complex Langevin Simulation

Details On the Segregation Phenomenon in Complex Langevin Simulation On the Segregation Phenomenon in Complex Langevin Simulation

1993-11-29

arxiv.org/abs/hep-th/9311174v1

Nucl.Phys. B424 (1994) 675-689

Physics

High Energy Physics

High Energy Physics - Theory

(20 pages + 8 figures on request). Siegen Si-93-8, Tokuyama TKYM-93-2

Scientific paper

10.1016/0550-3213(94)90413-8

In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree of freedom ($S=-\beta\cos\theta$). We find that the failure is not due to the defect of complex Langevin simulation itself, but rather to the way how one treats the singularity appearing in the drift force. An effective algorithm is proposed by which one can simulate the ${1/\beta}$ behaviour of the expectation value $<\cos\theta>$ in the small $\beta$ limit.

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