Predicting the Aoki Phase using the Chiral Lagrangian

Details Predicting the Aoki Phase using the Chiral Lagrangian Predicting the Aoki Phase using the Chiral Lagrangian

1998-08-27

arxiv.org/abs/hep-lat/9808047v1

Nucl.Phys.Proc.Suppl. 73 (1999) 234-236

Physics

High Energy Physics

High Energy Physics - Lattice

LATTICE98(spectrum), 3 pages, 2 figures, LaTex, uses espcrc2.sty

Scientific paper

10.1016/S0920-5632(99)85033-6

This work is concerned with the phase diagram of Wilson fermions in the mass and coupling constant plane for two-flavor (unquenched) QCD. We show that as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian, supplemented by additional terms proportional to powers of the lattice spacing. We find two possible phase structures at non-zero lattice spacing: (1) There is an Aoki phase of spontaneously broken flavor and parity, with two massless Goldstone-pions, and a width $\Delta m_0 \sim a^3$; (2) There is no spontaneous symmetry breaking, and all three pions have equal mass of order $a$. Present numerical simulations suggest that the former option is realized.

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