31 citations · 144 across the 27 of their papers we have counts for
16 papers · 1 filter
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_{…
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…
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…
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…
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…
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…
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…
On the convergence of cluster expansions for polymer gases
Rodrigo Bissacot, Roberto Fernández, Aldo Procacci
We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subse…
Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields
Rodrigo Bissacot, Leandro Cioletti
In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercub…