New universality classes for two-dimensional σ-models

Sergio Caracciolo; Robert G. Edwards; Andrea Pelissetto; Alan D. Sokal

doi:10.1016/0920-5632(94)90328-X

New universality classes for two-dimensional σ-models

Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

We argue that the two-dimensional O(N)-invariant lattice σ-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum σ-model constructed by conventional pertubation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for N = 3, 4 on lattices up to 512 × 512, using a Wolff-type embedding algorithm. The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the RP^N-1 and N-vector models do not lie in the same universality class.

Original language	English (US)
Pages (from-to)	129-134
Number of pages	6
Journal	Nuclear Physics B (Proceedings Supplements)
Volume	34
Issue number	C
DOIs	https://doi.org/10.1016/0920-5632(94)90328-X
State	Published - Apr 1994

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Nuclear and High Energy Physics

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@article{440a3f0f75d340ce898c1a257d85a064,

title = "New universality classes for two-dimensional σ-models",

abstract = "We argue that the two-dimensional O(N)-invariant lattice σ-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum σ-model constructed by conventional pertubation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for N = 3, 4 on lattices up to 512 × 512, using a Wolff-type embedding algorithm. The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the RPN-1 and N-vector models do not lie in the same universality class.",

author = "Sergio Caracciolo and Edwards, {Robert G.} and Andrea Pelissetto and Sokal, {Alan D.}",

note = "Funding Information: We wish to thank M. Aizenman, P. Butera, M. Campostrini, M. Caselle, M. Creutz, C. De-stri, F. Gliozzi, P. Hasenfratz, H. Kunz, M. Lfischer, F. Niedermayer, G. Parisi, P. Pasini, D. Rokhsar, P. Rossi, E. Sefler, T. Spencer, E. Vi-cari, U. Wolff, G. Zumbach and D. Zwanziger for helpful discussions. Computations were performed at SCRI, NYU, SNS, the Universit/L di Pisa and the Pittsburgh Supercomputer Center. The authors' research was supported in part by the INFN and CNR, DOE contracts DE-FC05-85ER250000 and DE-FG02-90ER40581, NSF grants DMS-8911273 and DMS-9200719, NATO grant CRG 910251, and a grant from the NYU Research Challenge Fund.",

year = "1994",

month = apr,

doi = "10.1016/0920-5632(94)90328-X",

language = "English (US)",

volume = "34",

pages = "129--134",

journal = "Nuclear Physics B (Proceedings Supplements)",

issn = "0920-5632",

publisher = "Elsevier B.V.",

number = "C",

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T1 - New universality classes for two-dimensional σ-models

AU - Caracciolo, Sergio

AU - Edwards, Robert G.

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

N1 - Funding Information: We wish to thank M. Aizenman, P. Butera, M. Campostrini, M. Caselle, M. Creutz, C. De-stri, F. Gliozzi, P. Hasenfratz, H. Kunz, M. Lfischer, F. Niedermayer, G. Parisi, P. Pasini, D. Rokhsar, P. Rossi, E. Sefler, T. Spencer, E. Vi-cari, U. Wolff, G. Zumbach and D. Zwanziger for helpful discussions. Computations were performed at SCRI, NYU, SNS, the Universit/L di Pisa and the Pittsburgh Supercomputer Center. The authors' research was supported in part by the INFN and CNR, DOE contracts DE-FC05-85ER250000 and DE-FG02-90ER40581, NSF grants DMS-8911273 and DMS-9200719, NATO grant CRG 910251, and a grant from the NYU Research Challenge Fund.

PY - 1994/4

Y1 - 1994/4

N2 - We argue that the two-dimensional O(N)-invariant lattice σ-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum σ-model constructed by conventional pertubation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for N = 3, 4 on lattices up to 512 × 512, using a Wolff-type embedding algorithm. The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the RPN-1 and N-vector models do not lie in the same universality class.

AB - We argue that the two-dimensional O(N)-invariant lattice σ-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum σ-model constructed by conventional pertubation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for N = 3, 4 on lattices up to 512 × 512, using a Wolff-type embedding algorithm. The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the RPN-1 and N-vector models do not lie in the same universality class.

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JO - Nuclear Physics B (Proceedings Supplements)

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New universality classes for two-dimensional σ-models

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