Universal Phenomenology at Critical Exceptional Points of Nonequilibrium <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> Models

Abstract

In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="normal">O</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:math> field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mn>2</f:mn><f:mi>N</f:mi><f:mo>−</f:mo><f:mn>3</f:mn></f:math> Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>d</h:mi><h:mo>&lt;</h:mo><h:mn>4</h:mn></h:math> they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>N</j:mi><j:mo>=</j:mo><j:mn>2</j:mn></j:math>, and a generalization for arbitrary <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>N</l:mi></l:math>, which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>x</n:mi><n:mi>y</n:mi></n:math> magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium. Published by the American Physical Society 2024

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