03.01.2015 Views

Joint Institute for Nuclear Research Relativistic ... - Index of - JINR

Joint Institute for Nuclear Research Relativistic ... - Index of - JINR

Joint Institute for Nuclear Research Relativistic ... - Index of - JINR

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

where A is surface coefficient, B is volume coefficient, S is area surface, V is volume <strong>of</strong><br />

cube.<br />

For small surface we have good statistic and bad approximation. There<strong>for</strong>e we studied<br />

dependence <strong>of</strong> coefficient A,B from quantity use point in fitting. We discard n first point<br />

<strong>for</strong> small surface and the remaining points are fitted by dependence (10). Figure 3 is<br />

shown that. Small quantity <strong>of</strong> use point makes big dispersion <strong>for</strong> coefficient A,B, thus<br />

we can’t use them in analysis. The most appropriate area <strong>for</strong> conclusion is singled out<br />

by red solid rectangle. It turns, that Witten parameter depend from area surface and<br />

volume in two phases. Consequently it isn’t the order parameter <strong>for</strong> phase transition<br />

confinement-deconfinement.<br />

The result is multilevel algorithm stated on the close surface. This algorithm is tested<br />

on the Witten parameter calculating. Accuracy increased by two orders <strong>of</strong> magnitude<br />

with respect calculating without the use <strong>of</strong> the algorithm. Finally, Witten parameter<br />

isn’t the order parameter <strong>for</strong> phase transition confinement-deconfinement.<br />

References<br />

[1] Chernodub, M., and Polikarpov, M. Abelian projections and monopoles.<br />

arXiv:hep-th/9710205 [hep-th].<br />

[2] ’t Ho<strong>of</strong>t, G. Topology <strong>of</strong> the gauge condition and new confinement phases in<br />

non-abelian gauge theories. <strong>Nuclear</strong> Physics B 190, 3 (1981), 455 – 478.<br />

[3] Gukov, S. Phases <strong>of</strong> gauge theories and surface operators, 11-15 August 2008. The<br />

talk presented at the Prestrings, 11-15 August, 2008, Zürich, Switzerland.<br />

[4] Gukov, S., and Witten, E. Gauge theory, ramification, and the geometric langlands<br />

program. arXiv:hep-th/0612073v2 [hep-th].<br />

[5] Gukov, S., and Witten, E. Rigid surface operators. arXiv:0804.1561 [hep-th].<br />

[6] Lüscher, M., and Weisz, P. Locality and exponential error reduction in numerical<br />

lattice gauge theory. JHEP 0109 (2001), 010.<br />

[7] Parisi, G., Petronzio, R., and Rapuano, F. A measurement <strong>of</strong> the string<br />

tension near the continuum limit. Physics Letters B 128, 6 (1983), 418 – 420.<br />

56

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!