Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 018, 7 pages      hep-lat/0702016      https://doi.org/10.3842/SIGMA.2007.018
Contribution to the Proceedings of the O'Raifeartaigh Symposium

Lattice Field Theory with the Sign Problem and the Maximum Entropy Method

Masahiro Imachi a, Yasuhiko Shinno b and Hiroshi Yoneyama c
a) Kashiidai, Higashi-ku, Fukuoka, 813-0014, Japan
b) Takamatsu National College of Technology, Takamatsu 761-8058, Japan
c) Department of Physics, Saga University, Saga, 840-8502, Japan

Received September 30, 2006, in final form January 19, 2007; Published online February 05, 2007

Abstract
Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the θ term. We reconsider this problem from the point of view of the maximum entropy method.

Key words: lattice field theory; sign problem; maximum entropy method.

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References

  1. Bryan R.K., Maximum entropy analysis of oversampled data problems, Eur. Biophys. J. 18 (1990), 165-174.
  2. Jarrell M., Gubernatis J.E., Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data, Phys. Rep. 269 (1996), 133-195.
  3. Asakawa M., Hatsuda T., Nakahara Y., Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nuclear Phys. 46 (2001), 459-508, hep-lat/0011040.
  4. Imachi M., Shinno Y., Yoneyama H., Maximum entropy method approach to q term, Progr. Theoret. Phys. 111 (2004), 387-411, hep-lat/0309156.
  5. Imachi M., Shinno Y., Yoneyama H., True or fictitious flattening?: MEM and the q term, hep-lat/0506032.
  6. Imachi M., Shinno Y., Yoneyama H., Sign problem and MEM in lattice field theory with the q term, Progr. Theoret. Phys. 115 (2006), 931-949, hep-lat/0602009.
  7. 't Hooft G., Topology of the gauge condition and new confinement phases in non-Abelian gauge theories, Nuclear Phys. B 190 (1981), 455-478.
  8. Cardy J.L., Rabinovici E., Phase structure of Zp models in the presence of a q parameter, Nuclear Phys. B 205 (1982), 1-16.
  9. Cardy J. L., Duality and the parameter in Abelian lattice models, Nuclear Phys. B 205 (1982), 17-26.
  10. Seiberg N., Topology in strong coupling, Phys. Rev. Lett. 53 (1984), 637-640.
  11. Bhanot G., Rabinovici E., Seiberg N., Woit P., Lattice vacua, Nuclear Phys. B 230 (1984), 291-298.
  12. Wiese U.-J., Numerical simulation of lattice q-vacua: the 2-d U(1) gauge theory as a test case, Nuclear Phys. B 318 (1989), 153-175.
  13. Plefka J.C., Samuel S., Monte Carlo studies of two-dimensional systems with a q term, Phys. Rev. D 56 (1997), 44-54, hep-lat/9704016.
  14. Imachi M., Kanou S., Yoneyama H., Two-dimensional CP2 model with q term and topological charge distributions, Progr. Theoret. Phys. 102 (1999), 653-670, hep-lat/9905035.
  15. Hasenfratz P., Niedermayer F., Perfect lattice action for asymptotically free theories, Nuclear Phys. B 414 (1994), 785-814,hep-lat/9308004.
  16. Burkhalter R., Imachi M., Shinno Y., Yoneyama H., CPN-1 models with q term and fixed point action Progr. Theoret. Phys. 106 (2001), 613-640, hep-lat/0103016.


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