|
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.
pdf (622 kb)
ps (434 kb)
tex (664 kb)
References
- Bryan R.K., Maximum entropy analysis of oversampled data problems, Eur. Biophys. J. 18 (1990), 165-174.
- Jarrell M., Gubernatis J.E., Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data, Phys. Rep. 269 (1996), 133-195.
- 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.
- Imachi M., Shinno Y., Yoneyama H., Maximum entropy method approach to q term, Progr. Theoret. Phys. 111 (2004), 387-411, hep-lat/0309156.
- Imachi M., Shinno Y., Yoneyama H., True or fictitious flattening?: MEM and the q term, hep-lat/0506032.
- 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.
- 't Hooft G., Topology of the gauge condition and new confinement phases in non-Abelian gauge theories, Nuclear Phys. B 190 (1981), 455-478.
- Cardy J.L., Rabinovici E., Phase structure of Zp models in the presence of a q parameter, Nuclear Phys. B 205 (1982), 1-16.
- Cardy J. L., Duality and the parameter in Abelian lattice models, Nuclear Phys. B 205 (1982), 17-26.
- Seiberg N., Topology in strong coupling, Phys. Rev. Lett. 53 (1984), 637-640.
- Bhanot G., Rabinovici E., Seiberg N., Woit P.,
Lattice vacua, Nuclear Phys. B 230 (1984), 291-298.
- 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.
- 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.
- 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.
- Hasenfratz P., Niedermayer F., Perfect lattice action for asymptotically free theories, Nuclear Phys. B 414 (1994), 785-814,hep-lat/9308004.
- 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.
|
|