Isospin breaking and the chiral condensate

Abstract

With two degenerate quarks, the chiral condensate exhibits a jump as the quark masses pass through zero. I discuss how this single transition splits into two Ising like transitions when the quarks are made non-degenerate. The order parameter is the expectation of the neutral pion field. The transitions represent long distance coherent phenomena occuring without the Dirac operator having vanishingly small eigenvalues.

Comments: 6 pages, 3 figures; contribution to the XXIIIrd International Symposium on Lattice Field Theory, 25-30 July 2005, Trinity College, Dublin, Ireland