6 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,…
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…
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 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…
Extendable Shift Maps and Weighted Endomorphisms on Generalized Countable Markov Shifts
Rodrigo Bissacot, Iván Diaz-Granados, Thiago Raszeja
We obtain an operator algebraic characterization for when we can continuously extend the shift map from a standard countable Markov shift to its respective generalized count…
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 ferromagne…