31 citations · 144 across the 27 of their papers we have counts for
28 papers
A Cluster Expansion and the Decay of Correlations of the 1D Long-Range Ising Model at Low Temperatures
Rodrigo Bissacot, Henrique Corsini
In this work, a convergent low-temperature cluster expansion of the one-dimensional long-range ferromagnetic Ising model with polynomial decay is developed; that is, $…
Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models
Lucas Affonso, Rodrigo Bissacot, João Maia +2
We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{…
Extendable Shift Maps and the Canonical Map on Generalized Countable Markov Shifts
Rodrigo Bissacot, Iván Diaz-Granados, Thiago Raszeja
We obtain an operator-algebraic characterization of when the shift map can be continuously extended from a standard countable Markov shift to its generalized countable Markov…
Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours
Lucas Affonso, Rodrigo Bissacot, Henrique Corsini +1
Following seminal work by J. Fröhlich and T. Spencer on the critical exponent , we give a proof via contours of phase transition in the one-dimensional long-range ferromagneti…
Phase Transition in Long-Range state Models via Contours. Clock and Potts Models with Fields
Lucas Affonso, Rodrigo Bissacot, Gilberto Faria +1
Using the group structure of the state space of state models, a new definition of contour for long-range spin-systems in (), and a multidimensional version of F…
Phase Transitions in the semi-infinite Ising model with a decaying field
Rodrigo Bissacot, João Maia
We study the semi-infinite Ising model with an external field , is the wall influence, and . This external field decays as it gets further away from the…
Gibbs Measures on Multidimensional Spaces. Equivalences and a Groupoid Approach
Rodrigo Bissacot, Bruno Hideki Fukushima-Kimura, Rafael Pereira Lima +1
We consider some of the main notions of Gibbs measures on subshifts introduced by different communities, such as dynamical systems, probability, operator algebras, and mathematical…
Phase Transitions in Multidimensional Long-Range Random Field Ising Models
Lucas Affonso, Rodrigo Bissacot, João Maia
We extend a recent argument by Ding and Zhuang from nearest-neighbor to long-range interactions and prove the phase transition in a class of ferromagnetic random field Ising models…
Thermodynamic formalism for amenable groups and countable state spaces
Elmer R. Beltrán, Rodrigo Bissacot, Luísa Borsato +1
Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tili…
Quantum Statistical Mechanics via Boundary Conditions. A Groupoid Approach to Quantum Spin Systems
Lucas Affonso, Rodrigo Bissacot, Marcelo Laca
We use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quan…
Zero-Temperature Chaos in Bidimensional Models with Finite-Range Potentials
Sebastián Barbieri, Rodrigo Bissacot, Gregório Dalle Vedove +1
We construct a finite-range potential on a bidimensional full shift on a finite alphabet that exhibits a zero-temperature chaotic behavior as introduced by van Enter and Ruszel. Th…
Long-Range Ising Models: Contours, Phase Transitions and Decaying Fields
Lucas Affonso, Rodrigo Bissacot, Eric O. Endo +1
Inspired by Fröhlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase…
Infinite DLR Measures and Volume-Type Phase Transitions on Countable Markov Shifts
Elmer R. Beltrán, Rodrigo Bissacot, Eric O. Endo
We consider the natural definition of DLR measure in the setting of -finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of confor…
Quasi-invariant measures for generalized approximately proper equivalence relations
R. Bissacot, R. Exel, R. Frausino +1
We introduce a generalization of the notion of approximately proper equivalence relations studied by Renault and with it we build an étale groupoid. Choosing a suitable set of cont…
Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States
Rodrigo Bissacot, Ruy Exel, Rodrigo Frausino +1
Given a 0-1 infinite matrix and its countable Markov shift , one of the authors and M. Laca have introduced a kind of {\it generalized countable Markov shift} $X_A=Σ_A \cu…
Entropy Compression Method and Legitimate Colorings in Projective Planes
Rodrigo Bissacot, Luís Doin
We prove that the entropy compression method systematized by L. Esperet and A. Parreau [11] can be applied to any problem formulated in the variable version of the Lovász Local Lem…
Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields
Rodrigo Bissacot, Eric O. Endo, Aernout C. D. van Enter +2
We consider ferromagnetic long-range Ising models which display phase transitions. They are long-range one-dimensional Ising ferromagnets, in which the interaction is given by $J_{…
Entropic repulsion and lack of the -measure property for Dyson models
Rodrigo Bissacot, Eric Ossami Endo, Aernout C. D. van Enter +1
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not -measures. The…
Dyson models under renormalization and in weak fields
R. Bissacot, E. O. Endo, A. C. D. van Enter +3
We consider one-dimensional long-range spin models (usually called Dyson models), consisting of Ising ferromagnets with slowly decaying long-range pair potentials of the form $\fra…
A Large Deviation Principle for Gibbs States on Markov Shifts at Zero Temperature
Rodrigo Bissacot, Jairo K. Mengue, Edgardo Pérez
Let be a topologically mixing countable Markov shift with the BIP property over the alphabet and a po…
Stability of the Phase Transition of Critical-Field Ising Model on Cayley trees under Inhomogeneous External Fields
Rodrigo Bissacot, Eric Ossami Endo, Aernout C. D. van Enter
We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for…
Counting Contours on Trees
Noga Alon, Rodrigo Bissacot, Eric Ossami Endo
We calculate the exact number of contours of size containing a fixed vertex in -ary trees and provide sharp estimates for this number for more general trees. We also obtain…
Zero-temperature phase diagram for double-well type potentials in the summable variation class
Rodrigo Bissacot, Eduardo Garibaldi, Philippe Thieullen
We study the zero-temperature limit of the Gibbs measures of a class of long-range potentials on a full shift of two symbols . These potentials were introduced by Walters…
On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof
Rodrigo Bissacot, Ricardo Freire
We prove that if is an irreducible Markov shift space over and is coercive with bounded va…