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  • 1
    Electronic Resource
    Electronic Resource
    Some rigorous results on the phase diagram of the dilute Ising model
    Amsterdam : Elsevier
    Physics Letters A 94 (1983), S. 309-311 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0375-9601(83)90726-0
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  • 2
    Electronic Resource
    Electronic Resource
    A study of metastability in the Ising model (1974)
    Springer
    Communications in mathematical physics 39 (1974), S. 185-205 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a two-dimensional Ising ferromagnet with (+) boundary conditions and negative external field, where a Markovian time evolution is assumed. We construct, suitably restricting the allowed configurations att=0, a non equilibrium state with positive magnetization such that: 1) only one phase is present, 2) the relaxation time for unit volume is finite and can be made very large. These results are obtained following a general method for describing metastable states proposed by Lebowitz and Penrose and exploiting the analysis of the Ising-spin-configurations in terms of contours given by Minlos and Sinai.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01614240
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  • 3
    Electronic Resource
    Electronic Resource
    Some numerical results on the block spin transformation for the 2D Ising model at the critical point (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 731-757 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; renormalization group ; finite-size conditions ; critical point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the block spin transformation for the 2D Ising model at the critical temperatureT c . We consider the model with the constraint that the total spin in each block is zero. An old argument by Cassandro and Gallavotti strongly supports the Gibbsianness of the transformed measure, provided that such model has a critical temperatureT′ c lower thanT c . After describing a possible rigorous approach to the problem, we present numerical evidence that indeedT′ c 〈T c and study the Dobrushin-Shlosman uniqueness condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183686
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  • 4
    Electronic Resource
    Electronic Resource
    Couplings and Asymptotic Exponentiality of Exit Times (1998)
    Springer
    Journal of statistical physics 93 (1998), S. 393-404 
    Details
    ISSN: 1572-9613
    Keywords: Exit times ; exponentiality ; metastability ; couplings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin–Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:JOSS.0000026739.46334.05
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  • 5
    Electronic Resource
    Electronic Resource
    Instability of renormalization-group pathologies under decimation (1995)
    Springer
    Journal of statistical physics 79 (1995), S. 25-42 
    Details
    ISSN: 1572-9613
    Keywords: Renormalization group ; decimation ; non-Gibbsianness ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the stability and instability of pathologies of renormalization group transformations for lattice spin systems under decimation. In particular we show that, even if the original renormalization group transformation gives rise to a non-Gibbsian measure, Gibbsianness may be restored by applying an extra decimation transformation. This fact is illustrated in detail for the block spin transformation applied to the Ising model. We also discuss the case of another non-Gibbsian measure with nicely decaying correlations functions which remains non-Gibbsian after arbitrary decimation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179382
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  • 6
    Electronic Resource
    Electronic Resource
    Markov chains with exponentially small transition probabilities: First exit problem from a general domain. I. The reversible case (1995)
    Springer
    Journal of statistical physics 79 (1995), S. 613-647 
    Details
    ISSN: 1572-9613
    Keywords: Markov chains ; first exit problem ; large deviations ; reversibility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider general ergodic aperiodic Markov chains with finite state space whose transition probabilities between pairs of different communicating states are exponentially small in a large parameter β. We extend previous results by M. I. Freidlin and A. D. Wentzell (FW) on the first exit problem from a general domainQ. In the present paper we analyze the case ofreversible Markov chains. The general case will be studied in a forthcoming paper. We probe, in a purely probabilistic way and without using the FW graphical technique, some results on the first exit problem from a general domainQ containing many attractors. In particular we analyze the properties of special domains calledcycles and, by using the new concept oftemporal entropy, we obtain new results leading to a complete description of the typical tube of trajectories during the first excursion outsideQ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02184873
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  • 7
    Electronic Resource
    Electronic Resource
    Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II. The general case (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 987-1041 
    Details
    ISSN: 1572-9613
    Keywords: Markov chains ; first exit problem ; large deviations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we consider aperiodic ergodic Markov chains with transition probabilities exponentially small in a large parameter β. We extend to the general, not necessarily reversible case the analysis, started in part I of this work, of the first exit problem from a general domainQ containing many stable equilibria (attracting equilibrium points for the β=∞ dynamics). In particular we describe the tube of typical trajectories during the first excursion outsideQ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02174126
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  • 8
    Electronic Resource
    Electronic Resource
    Shapes of growing droplets—A model of escape from a metastable phase (1994)
    Springer
    Journal of statistical physics 75 (1994), S. 409-506 
    Details
    ISSN: 1572-9613
    Keywords: Stochastic dynamics ; Ising model ; next nearest neighbor interaction ; metastability ; crystal growth ; first excursion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Nucleation from a metastable state is studied for an Ising ferromagnet with nearest and next nearest neighbor interaction and at very low temperatures. The typical escape path is shown to follow a sequence of configurations with a growing droplet of stable phase whose shape is determined by dynamical considerations and differs significantly from the equilibrium shape corresponding to the instantaneous volume.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186869
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  • 9
    Electronic Resource
    Electronic Resource
    Approach to equilibrium of Glauber dynamics in the one phase region (1994)
    Springer
    Communications in mathematical physics 161 (1994), S. 447-486 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed. In particular somefinite size conditions are discussed, together with their implications for the Gibbs measures and for the approach to equilibrium of Glauber dynamics inarbitrarily large volumes. It is shown that Dobrushin-Shlosman's theory ofcomplete analyticity and its dynamical counterpart due to Stroock and Zegarlinski, cannot be applied, in general, to the whole one phase region since it requires mixing properties for regions ofarbitrary shape. An alternative approach, based on previous ideas of Oliveri, and Picco, is developed, which allows to establish results on rapid approach to equilibrium deeply inside the one phase region. In particular, in the ferromagnetic case, we considerably improve some previous results by Holley and Aizenman and Holley. Our results are optimal in the sene that, for example, they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed-dimensional Ising model with or without an external field. In part II we extensively consider the general case (not necessarily attractive) and we develop a new method, based on renormalizations group ideas and on an assumption of strong mixing in a finite cube, to prove hypercontractivity of the Markov semigroup of the Glauber dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101929
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  • 10
    Electronic Resource
    Electronic Resource
    For 2-D lattice spin systems weak mixing implies strong mixing (1994)
    Springer
    Communications in mathematical physics 165 (1994), S. 33-47 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that for finite range discrete spin systems on the two dimensional latticeZ 2, the (weak) mixing condition which follows, for instance, from the Dobrushin-Shlosman uniqueness condition for the Gibbs state implies a stronger mixing property of the Gibbs state, similar to the Dobrushin-Shlosman complete analyticity condition, but restricted to all squares in the lattice, or, more generally, to all sets multiple of a large enough square. The key observation leading to the proof is that a change in the boundary conditions cannot propagate either in the bulk, because of the weak mixing condition, or along the boundary because it is one dimensional. As a consequence we obtain for ferromagnetic Ising-type systems proofs that several nice properties hold arbitrarily close to the critical temperature; these properties include the existence of a convergent cluster expansion and uniform boundedness of the logarithmic Sobolev constant and rapid convergence to equilibrium of the associated Glauber dynamics on nice subsets ofZ 2, including the full lattice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099735
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