Modular invariance of finite size corrections and a vortex critical phase

doi:https://doi.org/10.1103/PhysRevLett.76.1196

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

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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:

Nash, C; OConnor, D ^[1]

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

Publication Date:: 1996-02-01

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.

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                    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

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                    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.

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@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}

}

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