Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at <math><mrow><mi mathvariant="normal">O</mi><msup><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mo>*</mo></msup></mrow></math> and <math><msup><mrow><mi>Ising</mi></mrow><mo>*</mo></msup></math> continuous transitions - INSPIRE

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Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at $O {(N)}^{}$ and ${Ising}^{}$ continuous transitions

Claudio Bonati
(
- Pisa U. and
- INFN, Pisa
)
,
Andrea Pelissetto
(
- INFN, Rome and
- Rome U.
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

May 22, 2024

15 pages

Published in:

Phys.Rev.B 110 (2024) 12, 125109

Published: Sep 6, 2024

e-Print:

2405.13485 [hep-lat]

DOI:

10.1103/PhysRevB.110.125109 (publication)

View in:

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Abstract: (APS)

We study the

O {(N)}^{*}

transitions that occur in the 3D

Z_{2}

-gauge

N

-vector model and the analogous

{Ising}^{*}

transitions occurring in the 3D

Z_{2}

-gauge Higgs model, corresponding to the

Z_{2}

-gauge

N

-vector model with

N = 1

. At these transitions, gauge-invariant correlations behave as in the usual

N

-vector (Ising for

N = 1

) model. Instead, the non-gauge-invariant spin correlations are trivial and therefore the spin order parameter that characterizes the spontaneous breaking of the

O (N)

symmetry in standard

N

-vector (Ising) systems is apparently absent. We define a gauge fixing procedure—we name it stochastic gauge fixing—that allows us to define a gauge-dependent vector field that orders at the transition and is therefore the appropriate order parameter for the

O (N)

symmetry breaking. To substantiate this approach, we perform numerical simulations for

N = 3

and

N = 1

. A finite-size scaling analysis of the numerical data allows us to confirm the general scenario: the gauge-fixed spin correlation functions behave as the corresponding functions computed in the usual

N

-vector (Ising) model. The emergence of a critical vector order parameter in the gauge model shows the complete equivalence of the

O {(N)}^{*}

(

{Ising}^{*}

) and

O (N)

(Ising) universality classes.

Note:

15 pages, 16 pdf figures, minor changes

gauge fixing: stochastic
invariance: gauge
spin: correlation
spin: correlation function
scaling: finite size
field theory: vector
Ising model
gauge dependence
universality
symmetry breaking

References(96)

Figures(16)

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