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Critical behavior induced by quenched disorder

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  • Nihat Berker, A.

Abstract

Domain arguments and renormalization-group calculations indicate that all temperature-driven symmetry-breaking first-order phase transitions are converted to second order by quenched bond randomness. This occurs for infinitesimal randomness in d⩽2 or d⩽4 respectively for discrete or continuous (n = 1 or n⩾2 component) microscopic degrees of freedom. Even strongly first-order transitions undergo this conversion to second order! Above these dimensions this conversion still occurs but requires a threshold bond randomness, presumably with an intervening new tricritical point. For example, q-state Potts transitions can be made second order for any q in any d, via bond randomness. Non-symmetry-breaking “temperature-driven” first-order transitions are eliminated under the above conditions. These quenched-fluctuation-induced second-order phase transitions suggest the possibility of new universality classes of criticality and tricriticality.

Suggested Citation

  • Nihat Berker, A., 1993. "Critical behavior induced by quenched disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 72-76.
    • Handle: RePEc:eee:phsmap:v:194:y:1993:i:1:p:72-76
    DOI: 10.1016/0378-4371(93)90341-Z
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    1. P. R. Cowley, 1988. "Market structure and business performance: An evaluation of buyer/seller power in the pims database," Strategic Management Journal, Wiley Blackwell, vol. 9(3), pages 271-278, May.
    2. Wehrung, Donald A & Lee, Kam-Hon & Tse, David K. & Vertinsky, Ilan B., 1989. "Adjusting Risky Situations: A Theoretical Framework and Empirical Test," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 189-212, June.
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    1. Türkoğlu, Alpar & Berker, A. Nihat, 2021. "Phase transitions of the variety of random-field Potts models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    2. Tamashiro, M.N. & Salinas, S.R.A., 1994. "A spin-S model on a Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 124-146.

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