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Universal behavior of coupled order parameters below three dimensions.

Julia Borchardt1, Astrid Eichhorn2

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This study reveals complex critical behaviors in competing order parameter models. In dimensions below three, multiple stable fixed points indicate the coexistence of various universality classes.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Field Theory

Background:

  • Investigating critical phenomena in systems with competing order parameters is crucial for understanding phase transitions.
  • The O(N) ⊕ O(M) symmetry describes a class of models relevant to diverse physical systems.

Purpose of the Study:

  • To explore universal critical behavior in models with two competing order parameters and O(N) ⊕ O(M) symmetry for dimensions d ≤ 3.
  • To uncover the detailed structure of renormalization group fixed points in lower dimensions.

Main Methods:

  • Utilizing pseudospectral techniques to solve functional renormalization group equations.
  • Analyzing field theories in a two-dimensional field space.

Main Results:

  • In d=3, a single stable fixed point (bicritical or tetracritical behavior) is consistently found.
  • In d<3, a more intricate fixed point structure emerges, with two additional bicritical fixed points identified.
  • For N=M approaching d=2, multiple simultaneously stable fixed points are discovered, signaling the coexistence of several universality classes.

Conclusions:

  • The critical behavior of these models becomes significantly richer in dimensions below three.
  • The coexistence of multiple universality classes is possible in specific parameter regimes (N=M) as dimensions approach two.