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Fluids in Random Media and Dimensional Augmentation.

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  • 1All Souls College, University of Oxford, Oxford OX1 4AL, United Kingdom and Department of Physics, University of California, Berkeley, California 94720, USA.

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|October 20, 2023
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Summary
This summary is machine-generated.

We solved the dimensional reduction puzzle in the random field Ising model. A d-dimensional system maps to a D=d+2 dimensional one with specific interaction and disorder properties.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • The random field Ising model (RFIM) presents challenges in understanding dimensional reduction.
  • Previous approaches often relied on replicas or perturbative field theory.

Purpose of the Study:

  • To resolve the dimensional reduction puzzle in the RFIM.
  • To identify the corresponding higher-dimensional random problem for a given d-dimensional system.

Main Methods:

  • Convergent cluster expansions were employed, avoiding replicas and perturbative field theory.
  • The Lee-Yang theorem was utilized to extend results to the critical point for lattice gas models.
  • The matrix-tree theorem provided a direct derivation path.

Main Results:

  • A d-dimensional continuum binary fluid and Ising lattice gas map to a D=d+2 dimensional model.
  • This D-dimensional model features infinite-range interactions and correlated disorder.
  • The mean density and other observables are shown to be equivalent.

Conclusions:

  • The proposed solution offers a non-perturbative understanding of dimensional reduction in the RFIM.
  • The findings are consistent with rigorous results on ordering in D=3 dimensions.
  • The method provides a novel approach using cluster expansions and the matrix-tree theorem.