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Hyperuniformity in Ashkin-Teller model.

Indranil Mukherjee1, P K Mohanty1

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Summary
This summary is machine-generated.

Equilibrium systems obeying Harris criterion show suppressed energy fluctuations at critical states. This finding applies to models like Ashkin-Teller, demonstrating hyperuniformity in energy and number fluctuations.

Keywords:
Ashkin–Teller modelHarris criterionhyperuniformitysupressed fluctuations

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Critical Phenomena

Background:

  • The Harris criterion (dν > 2) predicts suppressed energy fluctuations in critical systems.
  • The Ashkin-Teller model provides a framework to study critical phenomena in d=2 dimensions.
  • Understanding fluctuations is key to characterizing phase transitions and system stability.

Purpose of the Study:

  • To demonstrate suppressed energy fluctuations in systems satisfying the Harris criterion.
  • To analyze the Ashkin-Teller model's behavior when the Harris criterion is violated.
  • To investigate the emergence of hyperuniformity in both energy and number fluctuations.

Main Methods:

  • Analysis of equilibrium systems in d-dimensions, focusing on the Harris criterion (dν > 2).
  • Investigated the Ashkin-Teller model in d=2, varying the inter-spin interaction strength (λ).
  • Calculated the variance of subsystem energy and number fluctuations as a function of length scale (l).

Main Results:

  • Systems obeying dν > 2 exhibit suppressed energy fluctuations at their critical state.
  • In the Ashkin-Teller model with negative λ, the correlation length exponent ν violates the Harris criterion.
  • The variance of subsystem energy and number fluctuations scales as l^(d-α), with hyperuniformity exponent α = 2(1-ν-1).

Conclusions:

  • Violation of the Harris criterion leads to hyperuniformity, characterized by suppressed fluctuations.
  • The Ashkin-Teller model exemplifies how tuning parameters can lead to hyperuniform states.
  • Hyperuniformity is a general feature observed in both energy and point-configuration fluctuations under specific conditions.