56 citations · 203 across the 20 of their papers we have counts for
20 papers
On the Lyapunov exponent for the random field Ising transfer matrix, in the critical case
Orphée Collin, Giambattista Giacomin, Rafael L. Greenblatt +1
We study the top Lyapunov exponent of a product of random matrices appearing in the analysis of several statistical mechanical models with disorder, extending a previo…
The scaling limit of boundary spin correlations in non-integrable Ising models
Giulia Cava, Alessandro Giuliani, Rafael Leon Greenblatt
We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip…
The boundary disorder correlation for the Ising model on a cylinder
Rafael Leon Greenblatt
I give an expression for the correlation function of disorder insertions on the edges of the critical Ising model on a cylinder as a function of the aspect ratio (rescaled in the c…
On the spin interface distribution for non-integrable variants of the two-dimensional Ising model
Rafael L. Greenblatt, Eveliina Peltola
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…
Constructing a weakly-interacting fixed point of the Fermionic Polchinski equation
Rafael Leon Greenblatt
I rigorously prove the existence of a nontrivial fixed point of a family of continuous renormalization group flows corresponding to certain weakly interacting Fermionic quantum fie…
Adiabatic Evolution of Low-Temperature Many-Body Systems
Rafael L. Greenblatt, Markus Lange, Giovanna Marcelli +1
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-dependen…
The zeros of the partition function of the pinning model
Giambattista Giacomin, Rafael L. Greenblatt
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 processe…
Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case
Giambattista Giacomin, Rafael L. Greenblatt
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 exam…
Non-integrable Ising models in cylindrical geometry: Grassmann representation and infinite volume limit
Giovanni Antinucci, Alessandro Giuliani, Rafael L. Greenblatt
In this paper, meant as a companion to arXiv:2006.04458, we consider a class of non-integrable Ising models in cylindrical domains, and we discuss two key aspects of the multi…
Discrete and zeta-regularized determinants of the Laplacian on polygonal domains with Dirichlet boundary conditions
Rafael Leon Greenblatt
For a connected, open, bounded set whose boundary is a finite union of disjoint polygons whose vertices have integer coordinates, the logarithm of the discr…
Energy correlations of non-integrable Ising models: The scaling limit in the cylinder
Giovanni Antinucci, Alessandro Giuliani, Rafael Leon Greenblatt
We consider a class of non-integrable 2D Ising models, whose Hamiltonian, in addition to the nearest neighbor couplings, includes weak multi-spin interactions, even under spin flip…
Continuum limit of random matrix products in statistical mechanics of disordered systems
Francis Comets, Giambattista Giacomin, Rafael L. Greenblatt
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…
Singular behavior of the leading Lyapunov exponent of a product of random matrices
Giuseppe Genovese, Giambattista Giacomin, Rafael Leon Greenblatt
We consider a certain infinite product of random matrices appearing in the solution of some and dimensional disordered models in statistical mechanics, which…
The Ising model on a cylinder: universal finite size corrections and diagonalized action
Rafael L. Greenblatt
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 fie…
The scaling limit of the energy correlations in non integrable Ising models
Alessandro Giuliani, Rafael L. Greenblatt, Vieri Mastropietro
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…
Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
Michael Aizenman, Rafael L. Greenblatt, Joel L. Lebowitz
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 paramete…
Effects of Quenched Randomness on Classical and Quantum Phase Transitions
Rafael L. Greenblatt
This dissertation describes the effect of quenched randomness on first order phase transitions in lattice systems, classical and quantum. It is proven that a large class of quantum…
On Spin Systems with Quenched Randomness: Classical and Quantum
Rafael L Greenblatt, Michael Aizenman, Joel L. Lebowitz
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the…
Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
Rafael L. Greenblatt, Michael Aizenman, Joel L. Lebowitz
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 para…
Product Measure Steady States of Generalized Zero Range Processes
R. L. Greenblatt, J. L. Lebowitz
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…