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Journal of Applied Physics

Random-field mechanism in random-bond multicritical systems (abstract)

Kenneth Hui, A. Nihat Berker

Published May 1, 1990• 0 citations
Publisher

Abstract

It is argued on general grounds that bond randomness drastically alters multicritical phase diagrams via a random-field mechanism. For example, tricritical points and critical endpoints are entirely eliminated (in spatial dimension d≤2) or depressed in temperature (d>2). These predictions are confirmed by a renormalization-group calculation.1 Another consequence of this phenomenon is that, under bond randomness, the phase transitions of q-state Potts models are second order for all q at dimensionality d≤2.

DOI
10.1063/1.346040

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It is argued on general grounds that bond randomness drastically alters multicritical phase diagrams via a random-field mechanism. For example, tricritical points and critical endpoints are entirely eliminated (in spatial dimension d≤2) or depressed in temperature (d>2). These predictions are confirmed by a renormalization-group calculation.1 Another consequence of this phenomenon is that, under bond randomness, the phase transitions of q-state Potts models are second order for all q at dimensionality d≤2.
It is argued on general grounds that bond randomness drastically alters multicritical phase diagrams via a random-field mechanism. For example, tricritical points and critical end points are entirely eliminated (d\ensuremath{\le}2) or depressed in temperature (d>2). These predictions are confirmed by a renormalization-group calculation. Another consequence of this phenomenon is that, under bond randomness, the phase transitions of q-state Potts models are second order for all q at dimensionality d\ensuremath{\le}2.
Temperature-driven first-order phase transitions that involve symmetry breaking are converted to second order by the introduction of infinitesimal quenched bond randomness in spatial dimensions d≤2 or d≤4, respectively, for systems of n=1 or n≥ (R18)2 component microscopic degrees of freedom. Even strongly first-order transitions undergo this conversion to second order! Above these dimensions, this phenomenon still occurs, but requires a threshold amount of bond randomness. For example, under bond randomness, the phase transitions of q-state Potts models are second order for all q in d≤2. If no symmetry breaking is involved, temperature-driven first-order phase transitions are eliminated under the above conditions. Another consequence is that bond randomness drastically alters multicritical phase diagrams. Tricritical points and critical endpoints are entirely eliminated (d≤2) or depressed in temperature (d≳2). Similarly, bicritical phase diagrams are converted (d≤2) to reentrant-disorder-line or decoupled-tetracritical phase diagrams. These quenched-fluctuation-induced second-order transitions (a diametric opposite to the previously known annealed-fluctuation-induced first-order transitions) should lead to a multitude of new universality classes of criticality, including many experimentally accessible cases.
The effect of bond randomness on tricritical and critical end-point phenomena is studied by renormalization-group theory. In three dimensions, the pure-system tricritical point is replaced by a line segment of second-order transitions dominated by randomness and bounded by a multicritical point and a random-bond tricritical point, which reaches zero temperature at threshold randomness. This topology indicates a violation of the empirical universality principle. The random-bond tricritical point renormalizes onto the fixed distribution of random-field Ising criticality.
In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random magnetic fields on the tricritical phase diagram of the spin-1 Ising model in d=3d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3d=3. We find that random fields convert first-order phase transitions into second-order phase transitions more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent ${\ensuremath{\beta}}_{u}$. The random-field phase diagram is strikingly asymmetric. To accommodate this asymmetry, the second-order boundary exhibits reentrance.
We study the effect of varying strength $\ensuremath{\delta}$ of bond randomness on the phase transition of the three-dimensional Potts model for large qqq. The cooperative behavior of the system is determined by large correlated domains in which the spins point in the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\ensuremath{\delta}>{\ensuremath{\delta}}_{t}$ this percolating cluster coexists with a percolating cluster of noncorrelated spins. Such a coexistence is only possible in more than two dimensions. We argue and check numerically that ${\ensuremath{\delta}}_{t}$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as ${\ensuremath{\beta}}_{t}∕{\ensuremath{\nu}}_{t}=0.10(2)$ and ${\ensuremath{\nu}}_{t}=0.67(4)$. We claim these exponents are qqq independent for sufficiently large qqq. In the second-order transition regime the critical exponents ${\ensuremath{\beta}}_{t}∕{\ensuremath{\nu}}_{t}=0.60(2)$ and ${\ensuremath{\nu}}_{t}=0.73(1)$ are independent of the strength of disorder.