The spectral gap of the 2-D stochastic Ising model with mixed boundary conditions
Alexander, Kenneth S. ; Yoshida, Nobuo
arXiv, 0008201 / Harvested from arXiv
Text on arXiv
We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length n in the boundary is bounded by \delta n, where \delta < 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on \delta), the spectral gap decreases exponentially in n.
Publié le : 2000-08-25
Classification:  Mathematics - Probability,  Mathematical Physics,  60K35 (primary), 82C20 (secondary) 
@article{0008201,
     author = {Alexander, Kenneth S. and Yoshida, Nobuo},
     title = {The spectral gap of the 2-D stochastic Ising model with mixed boundary
  conditions},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0008201}
}

Alexander, Kenneth S.; Yoshida, Nobuo. The spectral gap of the 2-D stochastic Ising model with mixed boundary
  conditions. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0008201/