Modular invariance of finite size corrections and a vortex critical phase

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.76.1196· OSTI ID:285410

Nash, C; OConnor, D ^[1]

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1. Department of Mathematical Physics, St. Patrick`s College, Maynooth (Ireland)

We find the exact finite size and lattice corrections, to the partition function {ital Z}, of a continuous spin Gaussian model on a toroidal triangular lattice, with periods {ital L}{sub 0} and {ital L}{sub 1}. The spins carry a representation of the fundamental group of the torus labeled by {ital u}{sub 0} and {ital u}{sub 1} and mass {ital m}. Summing {ital Z}{sup {minus}1/2} over {ital u}{sub {ital i}} gives the corresponding result for the Ising model. The limits {ital m}{r_arrow}0 and {ital u}{sub {ital i}}{r_arrow}0 do not commute. With {ital m}=0 and {ital u}{sub {ital i}} nonzero the model exhibits a vortex critical phase. In the continuum limit, for arbitrary {ital m}, the finite size corrections to {minus}ln{ital Z} are modular invariant. In the limit {ital L}{sub 1{r_arrow}{infinity}} the {open_quote}{open_quote}cylinder charge{close_quote}{close_quote} {ital c}({ital u}{sub 0},{ital m}{sup 2}{ital L}{sup 2}{sub 0}) ranges nonmonotonically from 2[1+6{ital u}{sub 0}({ital u}{sub 0}{minus}1)] for {ital m}=0 to zero for {ital m}{r_arrow}{infinity}. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 285410
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 8 Vol. 76; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CORRECTIONS
CRITICALITY
ISING MODEL
PARTITION FUNCTIONS
SIZE
SPIN
VORTEX FLOW