Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs

Details Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs

1999-10-24

arxiv.org/abs/cond-mat/9910377v1

Phys. Rev. E60, 3512-3515 (1999)

Physics

Condensed Matter

Statistical Mechanics

8 pages, Latex, 2 postscript figures

Scientific paper

10.1103/PhysRevE.60.3512

The q-state Potts antiferromagnet on a lattice $\Lambda$ exhibits nonzero ground state entropy $S_0=k_B \ln W$ for sufficiently large q and hence is an exception to the third law of thermodynamics. An outstanding challenge has been the calculation of W(sq,q) on the square (sq) lattice. We present here an exact calculation of W on an infinite-length cyclic strip of the square lattice which embodies the expected analytic properties of W(sq,q). Similar results are given for the kagom\'e lattice.

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