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  • 1
    Electronic Resource
    Electronic Resource
    Phase diagram for the Bethe lattice spin glass (abstract) (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 4001-4001 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We present the results of rigorous calculations for the ±J Ising spin-glass model on the Bethe lattice. The phase diagram for varying temperature and fraction of ferromagnetic bonds is derived near the paramagnetic phase boundary. In addition to the spin-glass and paramagnetic phases, we find a nontrivial ferromagnetic phase and a magnetized spin-glass phase, characterized by diverging Edwards–Anderson susceptibility. The recursion relation for the distribution of single-site magnetizations is studied as a dynamical system on an appropriate function space, the bulk thermodynamics is described by the attractors of the recursion relation, and the phase transitions correspond to bifurcations in the dynamics. Using bifurcation theory, we establish the existence of a stable distribution of single-site magnetizations near the paramagnetic phase boundary. At least in single-site properties, the existence proof precludes chaos, and infinite hierarchy of transitions, and other conceivable bizarre possibilities. While our phase diagram is very similar to the phase diagram for the Sherrington–Kirkpatrick model, the Bethe lattice provides a useful description of the mean-field behavior of spin glasses because the interactions are short range, the analysis is much more straightforward, and the results have been made completely rigorous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.340577
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  • 2
    Electronic Resource
    Electronic Resource
    Nonperturbative analysis of a model of random surfaces
    Amsterdam : Elsevier
    Nuclear Physics, Section B 251 (1985), S. 553-564 
    Details
    ISSN: 0550-3213
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0550-3213(85)90277-9
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  • 3
    Electronic Resource
    Electronic Resource
    The correct extension of the Fortuin-Kasteleyn result to plaquette percolation
    Amsterdam : Elsevier
    Nuclear Physics, Section B 235 (1984), S. 19-23 
    Details
    ISSN: 0550-3213
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0550-3213(84)90145-7
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  • 4
    Electronic Resource
    Electronic Resource
    Aggregation and intermediate phases in dilute spin systems (1995)
    Springer
    Communications in mathematical physics 171 (1995), S. 203-232 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study a variety of dilute annealed lattice spin systems. For site diluted problems with many internal spin states, we uncover a new phase characterized by the occupation and vacancy of staggered sublattices. In cases where the uniform system has a low temperature phase, the staggered states represent an intermediate phase. Furthermore, in many of these cases, we show that (at least part of) the phase boundary separating the low-temperature and staggered phases is a line of phase coexistence-i.e. the transition is first order. We also study the phenomenon of aggregation (phase separation) in bond diluted models. Such transitions are known, trivially, to occur in the large-q Potts models. However, it turns out that phase separation is typical in bond diluted spin systems with many internal states. (In particular, a bond aggregation transition is not tied to a discontinuous transition in the uniform system.) Along the portions of the phase boundary where any of these phenomena occur, the prospects for a Fisher renormalization effect are deemed to be highly unlikely or are ruled out altogether.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02103776
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  • 5
    Electronic Resource
    Electronic Resource
    Non-Perturbative Criteria for Gibbsian Uniqueness (1997)
    Springer
    Communications in mathematical physics 189 (1997), S. 447-464 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: For spin-systems with an internal symmetry, we provide sufficient conditions for unicity of the Gibbs state and/or complete analyticity by comparison to random cluster models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050210
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  • 6
    Electronic Resource
    Electronic Resource
    Staggered Phases in Diluted Systems with Continuous Spins (1997)
    Springer
    Communications in mathematical physics 189 (1997), S. 631-640 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We consider systems with continuous spins and annealed dilution. We show that, as in the discrete case, such systems often undergo a phase transition, which is manifested in the appearance of a staggered intermediate phase. In particular, these phases appear in systems such as the massive Gaussian model where there is no phase transition in the undiluted system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050221
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  • 7
    Electronic Resource
    Electronic Resource
    Absence of pair binding in the U=∞ Hubbard model (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 265-270 
    Details
    ISSN: 1573-0530
    Keywords: 82B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the standard Hubbard model in the U=∞ limit. We show that, for any finite lattice with all positive hopping matrix elements, t i,j 〉0, the ground state energy of the system containing two particles in excess of half filling plus the energy of the system at half filling is never lower than twice the energy of the system with a single extra particle. Similar results are obtained for ‘holes’ when the lattice is bipartite. As a byproduct, we obtain a simple alternative proof of Tasaki's generalization of the Nagaoka theorem for non-bipartite lattices (but without the uniqueness clause).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398823
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  • 8
    Electronic Resource
    Electronic Resource
    Mean-Field Theory for Percolation Models of the Ising Type (1999)
    Springer
    Journal of statistical physics 94 (1999), S. 53-66 
    Details
    ISSN: 1572-9613
    Keywords: ising model ; percolation ; mean-field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The q=2 random cluster model is studied in the context of two mean-field models: the Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values as the critical point is approached from the high-density side, which vindicates the results of earlier studies. In particular, the exponent γ~′ which characterizes the divergence of the average size of finite clusters is 1/2, and ν~′, the exponent associated with the length scale of finite clusters, is 1/4. The full collection of exponents indicates an upper critical dimension of 6. The standard mean field exponents of the Ising system are also present in this model (ν′=1/2, γ′=1), which implies, in particular, the presence of two diverging length-scales. Furthermore, the finite cluster exponents are stable to the addition of disorder, which, near the upper critical dimension, may have interesting implications concerning the generality of the disordered system/correlation length bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004555127906
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  • 9
    Electronic Resource
    Electronic Resource
    Exponential decay of connectivities in the two-dimensional ising model (1987)
    Springer
    Journal of statistical physics 49 (1987), S. 433-445 
    Details
    ISSN: 1572-9613
    Keywords: Two-dimensional Ising model ; percolation ; exponential decay ; FK representation ; correlation lengths large deviations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove some results concerning the decay of connectivities in the low-temperature phase of the two-dimensional Ising model. These provide the bounds necessary to establish, nonperturbatively, large-deviation properties for block magnetizations in these systems. We also obtain estimates on the rate at which the finite-volume, plus-boundary-condition expectation of the spin at the origin converges to the spontaneous magnetization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01009344
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  • 10
    Electronic Resource
    Electronic Resource
    Convergence to Equilibrium of Random Ising Models in the Griffiths Phase (1998)
    Springer
    Journal of statistical physics 92 (1998), S. 337-351 
    Details
    ISSN: 1572-9613
    Keywords: Random spin systems ; diluted Ising model ; Glauber dynamics ; relaxation time ; Griffiths singularities ; FK representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider Glauber-type dynamics for disordered Ising spin systems with nearest neighbor pair interactions in the Griffiths phase. We prove that in a nontrivial portion of the Griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1. This condition has, in turn, been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential, and that the average over the disorder of the time-autocorrelation function goes to equilibrium faster than exp[−k(log t) d/(d−1)]. We then show that for the diluted Ising model these upper bounds are optimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023077101354
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