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Title: Modular invariance of finite size corrections and a vortex critical phase

Abstract

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.}

Authors:
;  [1]
  1. Department of Mathematical Physics, St. Patrick`s College, Maynooth (Ireland)
Publication Date:
OSTI Identifier:
285410
Resource Type:
Journal Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 76; Journal Issue: 8; Other Information: PBD: Feb 1996
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; VORTEX FLOW; CRITICALITY; SIZE; PARTITION FUNCTIONS; SPIN; ISING MODEL; CORRECTIONS

Citation Formats

Nash, C, OConnor, D, and School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4. Modular invariance of finite size corrections and a vortex critical phase. United States: N. p., 1996. Web. doi:10.1103/PhysRevLett.76.1196.
Nash, C, OConnor, D, & School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4. Modular invariance of finite size corrections and a vortex critical phase. United States. https://doi.org/10.1103/PhysRevLett.76.1196
Nash, C, OConnor, D, and School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4. Thu . "Modular invariance of finite size corrections and a vortex critical phase". United States. https://doi.org/10.1103/PhysRevLett.76.1196.
@article{osti_285410,
title = {Modular invariance of finite size corrections and a vortex critical phase},
author = {Nash, C and OConnor, D and School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4},
abstractNote = {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.}},
doi = {10.1103/PhysRevLett.76.1196},
url = {https://www.osti.gov/biblio/285410}, journal = {Physical Review Letters},
number = 8,
volume = 76,
place = {United States},
year = {1996},
month = {2}
}