# Manuel Gonzalez (Universidade de Sao Paulo)

We study the low-temperature phase diagram for a two-dimensional ferromagnetic Ising model, with a periodical external magnetic field. The external field takes two values: $h$ and $-h$. The sites associated with positive and negative values of external field mimic a configuration like a chessboard with rectangular cells of sides $L_1\times L_2$ sites, such that the total value of the external field is zero.

As a main result, we apply the reflection positivity method to show the presence of a first-order phase transition. In addition, we obtain a region of uniqueness for Gibbs measure, using a uniqueness condition obtained in terms of disagreement percolation.

Joint work with Eugene Pechersky (IITP/RAS) and Anatoly Yambartsev (IME/USP)

Sala 5, Facultad de Matemáticas, Puc Chile, 17:00 hrs.

##### Departamento de Matemáticas

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

##### Centro de Modelamiento Matemático (CMM)

Facultad de Ciencias Físicas y Matemáticas (FCFM)