2,632 research outputs found
Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
We prove that the addition of an arbitrarily small random perturbation of a
suitable type to a quantum spin system rounds a first order phase transition in
the conjugate order parameter in d <= 2 dimensions, or in systems with
continuous symmetry in d <= 4. This establishes rigorously for quantum systems
the existence of the Imry-Ma phenomenon, which for classical systems was proven
by Aizenman and Wehr.Comment: Four pages, RevTex. Minor correction
Continuum limit of random matrix products in statistical mechanics of disordered systems
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 which the leading Lyapunov exponent can be expressed
explicitly in terms of modified Bessel functions, a formula that appears in the
physical literature on these disordered systems. We provide an analysis of the
diffusion system as well as of the link with the matrix products. We then apply
the results to the framework considered by Derrida and Hilhorst [J. Phys. A
(1983)], which deals in particular with the strong interaction limit for
disordered Ising model in one dimension and that identifies a singular behavior
of the Lyapunov exponent (of the transfer matrix), and to the two dimensional
Ising model with columnar disorder (McCoy-Wu model). We show that the continuum
limit sharply captures the Derrida and Hilhorst singularity. Moreover we
revisit the analysis by McCoy and Wu [Phys. Rev. 1968] and remark that it can
be interpreted in terms of the continuum limit approximation. We provide a
mathematical analysis of the continuum approximation of the free energy of the
McCoy-Wu model, clarifying the prediction (by McCoy and Wu) that, in this
approximation, the free energy of the two dimensional Ising model with columnar
disorder is but not analytic at the critical temperature.Comment: 46 pages, one figure. Introduction reorganized, Proposition 1.5
corrects Proposition 1.6 of v2. Several other scattered modification
What\u27s Dignity Got to Do with It?: Using Anti-Commandeering Principles to Preserve State Sovereign Immunity
What\u27s Dignity Got to Do with It?: Using Anti-Commandeering Principles to Preserve State Sovereign Immunity
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Cardenio
Shakespeare's lost play, re-made in collaboration with the great Shakespeare scholar Stephen Greenblatt, and setâlike many of Shakespeare's romancesâin the hills of Italy. It has its own website (https://sites.fas.harvard.edu/~cardenio/index.html), where the Greenblatt/Mee re-make has also been re-made by others for productions in Croatia, Poland, Spain, Japan, India, Egypt, Serbia, Turkey, and Brazil, among other countries
Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case
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 Ising chain with random external field, and the free energy density of this Ising chain is the Lyapunov exponent we consider. We obtain the sharp behavior of this exponent in the large interaction limit when the external field is centered: this balanced case turns out to be critical in many respects. From a mathematical standpoint we precisely identify the behavior of the top Lyapunov exponent of a product of two dimensional random matrices close to a diagonal random matrix for which top and bottom Lyapunov exponents coincide. In particular, the Lyapunov exponent is only log-Hölder continuous
Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
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 continuous symmetry the statement extends up to d<=4 dimensions.
This establishes for quantum systems the existence of the Imry-Ma phenomenon
which for classical systems was proven by Aizenman and Wehr. The extension of
the proof to quantum systems is achieved by carrying out the analysis at the
level of thermodynamic quantities rather than equilibrium states.Comment: This article presents the detailed derivation of results which were
announced in Phys. Rev. Lett. 103 (2009) 197201 (arXiv:0907.2419). v3
incorporates many corrections and improvements resulting from referee
comment
The Zeros of the Partition Function of the Pinning Model
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 for rather general inter-arrival laws, but we achieve a substantially more complete understanding for a specific one parameter family of inter-arrivals. We show, for such a specific family, that the zeros asymptotically lie on (and densely fill) a closed curve that, unsurprisingly, touches the real axis only in one point (the critical point of the model). We also perform a sharper analysis of the zeros close to the critical point and we exploit this analysis to approach the challenging problem of Griffiths singularities for the disordered pinning model. The techniques we exploit are both probabilistic and analytical. Regarding the first, a central role is played by limit theorems for heavy tail random variables. As for the second, potential theory and singularity analysis of generating functions, along with their interplay, will be at the heart of several of our arguments
Product Measure Steady States of Generalized Zero Range Processes
We establish necessary and sufficient conditions for the existence of
factorizable steady states of the Generalized Zero Range Process. This process
allows transitions from a site to a site involving multiple particles
with rates depending on the content of the site , the direction of
movement, and the number of particles moving. We also show the sufficiency of a
similar condition for the continuous time Mass Transport Process, where the
mass at each site and the amount transferred in each transition are continuous
variables; we conjecture that this is also a necessary condition.Comment: 9 pages, LaTeX with IOP style files. v2 has minor corrections; v3 has
been rewritten for greater clarit
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