On simulating complex actions |
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| Institution: | 1. Department of Mathematics, University of Connecticut, 341 Mansfield Road, Storrs, CT 06269, United States;2. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, United States;3. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, United States;4. Department of Mathematics, Department of Statistics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, United States;1. University of Debrecen, Institute of Physics, H-4010 Debrecen P.O. Box 105, Hungary;2. MTA-DE Particle Physics Research Group, P.O. Box 51, H-4001 Debrecen, Hungary;3. Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen, Hungary;1. University of Wisconsin-Madison, Van Vleck Hall, United States of America;2. Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shandong, 266237, China;3. School of Mathematics, Shandong University, Jinan, Shandong, 250100, China;4. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, 119076 Singapore;5. Department of Mathematics, Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa Macao, China;6. UMacau Zhuhai Research Institute, Zhuhai, China;1. Dept. of Math., U. of Toronto, Toronto, ON, M5S 2E4, Canada;2. Dept. of Math., U. of Arizona, Tucson, AZ, 85721-0089, USA;3. Dept. of Math. & Stats., U. of Saskatchewan, Saskatoon, SK, S7N 5E6, Canada |
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| Abstract: | We describe and compare various methods to numerically simulate measures that are non-positive definite. We argue that variations of importance sampling will fail for large enough volume but some type of Riemann integration scheme might work. Using exact results for the three-dimensional Ising model, we show that to get anything distinguishable from noise, the phase of the measure must be known extremely precisely. We suggest that a recent method to compute the density of states may be the best method to use. |
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