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pro vyhledávání: '"Greenblatt, Rafael L."'
We point out that the construction of a martingale observable describing the spin interface of the two-dimensional Ising model extends to a class of non-integrable variants of the two-dimensional Ising model, and express it in terms of Grassmann inte
Externí odkaz:
http://arxiv.org/abs/2404.12375
Publikováno v:
Commun. Math. Phys. 405, 75 (2024)
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we
Externí odkaz:
http://arxiv.org/abs/2211.16836
Publikováno v:
Mathematical Physics, Analysis and Geometry volume 25, Article number: 16 (2022)
We aim at understanding for which (complex) values of the potential the pinning partition function vanishes. The pinning model is a Gibbs measure based on discrete renewal processes with power law inter-arrival distributions. We obtain some results f
Externí odkaz:
http://arxiv.org/abs/2107.11804
Publikováno v:
ALEA, Lat. Am. J. Probab. Math. Stat. vol. 19, pp. 701-728 (2022)
We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest neighbor
Externí odkaz:
http://arxiv.org/abs/2105.00018
Publikováno v:
Annales Henri Poincar\'e 23 (2022), 1061-1139
In this paper, meant as a companion to arXiv:2006.04458, we consider a class of non-integrable $2D$ Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a
Externí odkaz:
http://arxiv.org/abs/2104.09328
Publikováno v:
Commun. Math. Phys. 369:171-219 (2019)
We consider a particular weak disorder limit ("continuum limit") of matrix products that arise in the analysis of disordered statistical mechanics systems, with a particular focus on random transfer matrices. The limit system is a diffusion model for
Externí odkaz:
http://arxiv.org/abs/1712.09373
Akademický článek
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Autor:
Greenblatt, Rafael L.
Finite size corrections to the pressure (free energy) of the Ising model on a 2 dimensional cylinder are calculated and shown to be consistent with the predictions of conformal field theory. The exact solution of the model is expressed in terms of th
Externí odkaz:
http://arxiv.org/abs/1409.1852
Publikováno v:
J. Math. Phys. 53, 095214 (2012)
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling limit in
Externí odkaz:
http://arxiv.org/abs/1204.4040
Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
Publikováno v:
J. Math. Phys. 53, 023301 (2012)
We prove that for quantum lattice systems in d<=2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T=0. For systems with continuo
Externí odkaz:
http://arxiv.org/abs/1104.3515