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Dive into the research topics where Dmitry Ioffe is active.

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Featured researches published by Dmitry Ioffe.


Journal of Statistical Physics | 1994

Large deviations for the 2D ising model: A lower bound without cluster expansions

Dmitry Ioffe

We show that a lower large-deviation bound for the block-spin magnetization in the 2D Ising model can be pushed all the way forward toward its correct “Wulff” value for all β>βc.


Probability Theory and Related Fields | 1995

Exact large deviation bounds up toT c for the Ising model in two dimensions

Dmitry Ioffe

SummaryWe prove an upper large deviation bound for the block spin magnetization in the 2D Ising model in the phase coexistence region. The precise rate (given by the Wulff construction) is shown to hold true for all β > βc. Combined with the lower bounds derived in [I] those results yield an exact second order large deviation theory up to the critical temperature.


Letters in Mathematical Physics | 1996

On the extremality of the disordered state for the Ising model on the Bethe lattice

Dmitry Ioffe

We give a simple proof that the limit Ising Gibbs measure with free boundary conditions on the Bethe lattice with the forward branching ratio k≥2 is extremal if and only if β is less or equal to the spin glass transition value, given by tanh(βcSG= 1/√k.


Probability Theory and Related Fields | 2003

Ornstein-Zernike theory for finite range Ising models above T c

Massimo Campanino; Dmitry Ioffe; Yvan Alain Velenik

Abstract. We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈Σ0Σx〉β in the general context of finite range Ising type models on ℤd. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in the whole of the high temperature region β<βc. As a byproduct we obtain that for every β<βc, the inverse correlation length ξβ is an analytic and strictly convex function of direction.


Annals of Probability | 2008

Fluctuation theory of connectivities for subcritical random cluster models

Massimo Campanino; Dmitry Ioffe; Yvan Alain Velenik

We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional chains of irreducible objects. Statistics of local observables, for example, displacement, over such chains obey classical limit laws, and our construction leads to an effective random walk representation of percolation clusters. The results include a derivation of a sharp Ornstein–Zernike type asymptotic formula for two point functions, a proof of analyticity and strict convexity of inverse correlation length and a proof of an invariance principle for connected clusters under diffusive scaling. In two dimensions duality considerations enable a reformulation of these results for supercritical nearest-neighbor random cluster measures, in particular, for nearest-neighbor Potts models in the phase transition regime. Accordingly, we prove that in two dimensions Potts equilibrium crystal shapes are always analytic and strictly convex and that the interfaces between different phases are always diffusive. Thus, no roughening transition is possible in the whole regime where our results apply. Our results hold under an assumption of exponential decay of finite volume wired connectivities [assumption (1.2) below] in rectangular domains that is conjectured to hold in the whole subcritical regime; the latter is known to be true, in any dimensions, when q=1, q=2, and when q is sufficiently large. In two dimensions assumption (1.2) holds whenever there is an exponential decay of connectivities in the infinite volume measure. By duality, this includes all supercritical nearest-neighbor Potts models with positive surface tension between ordered phases.


Annals of Probability | 2012

Crossing random walks and stretched polymers at weak disorder

Dmitry Ioffe; Yvan Alain Velenik

We consider a model of a polymer in ℤd+1, constrained to join 0 and a hyperplane at distance N. The polymer is subject to a quenched nonnegative random environment. Alternatively, the model describes crossing random walks in a random potential (see Zerner [Ann Appl. Probab. 8 (1998) 246–280] or Chapter 5 of Sznitman [Brownian Motion, Obstacles and Random Media (1998) Springer] for the original Brownian motion formulation). It was recently shown [Ann. Probab. 36 (2008) 1528–1583; Probab. Theory Related Fields 143 (2009) 615–642] that, in such a setting, the quenched and annealed free energies coincide in the limit N → ∞, when d ≥ 3 and the temperature is sufficiently high. We first strengthen this result by proving that, under somewhat weaker assumptions on the distribution of disorder which, in particular, enable a small probability of traps, the ratio of quenched and annealed partition functions actually converges. We then conclude that, in this case, the polymer obeys a diffusive scaling, with the same diffusivity constant as the annealed model.


Archive | 2009

Stochastic Geometry of Classical and Quantum Ising Models

Dmitry Ioffe

These lecture notes are based on a mini-course which I taught at Prague school in September 2006. The idea was to try to develop and explain to probabilistically minded students a unified approach to the Fortuin-Kasteleyn (FK) and to the random current (RC) representation of classical and quantum Ising models via path integrals. No background in quantum statistical mechanics was assumed.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2003

Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder☆

Pietro Caputo; Dmitry Ioffe

Abstract Consider uniformly elliptic random walk on Z d with independent jump rates across nearest neighbour bonds of the lattice. We show that the infinite volume effective diffusion matrix can be almost surely recovered as the limit of finite volume periodized effective diffusion matrices.


Probability Theory and Related Fields | 2000

A note on the decay of correlations under δ-pinning

Dmitry Ioffe; Yvan Alain Velenik

We prove that for a class of massless


Archive | 1996

Extremality of the Disordered State for the Ising Model on General Trees

Dmitry Ioffe

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Senya Shlosman

Centre national de la recherche scientifique

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Lev Greenberg

Technion – Israel Institute of Technology

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Nicholas Crawford

Technion – Israel Institute of Technology

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