Glauber evolution with Kac potentials: II. Fluctuations

Nonlinearity ◽  
1996 ◽  
Vol 9 (1) ◽  
pp. 27-51 ◽  
Author(s):  
A De Masi ◽  
E Orlandi ◽  
E Presutti ◽  
L Triolo
Keyword(s):  
Kac Potentials

Travelling fronts in nonlocal models for phase separation in an external field

1997 ◽  
Vol 127 (4) ◽  
pp. 823-835 ◽  
Author(s):  
Enza Orlandi ◽  
Livio Triolo
Keyword(s):  
Magnetic Field ◽  
Metastable Phase ◽  
Glauber Dynamics ◽  
One Dimensional ◽  
Kac Potentials ◽  
Nonlocal Models ◽  
Nonlocal Evolution Equation ◽  
Travelling Fronts ◽  
The One ◽  
The Magnetic Field

We consider the one-dimensional, nonlocal, evolution equation derived by De Masi et al. (1995) for Ising systems with Glauber dynamics, Kac potentials and magnetic field. We prove the existence of travelling fronts, their uniqueness modulo translations among the monotone profiles and their linear stability for all the admissible values of the magnetic field for which the underlying spin system exhibits a stable and metastable phase.

Glauber evolution with Kac potentials: III. Spinodal decomposition

Nonlinearity ◽  
1996 ◽  
Vol 9 (1) ◽  
pp. 53-114 ◽  
Author(s):  
A De Masi ◽  
E Orlandi ◽  
E Presutti ◽  
L Triolo
Keyword(s):  
Spinodal Decomposition ◽  
Kac Potentials

scholarly journals Renewal properties of the d = 1 Ising model

2018 ◽  
Vol 30 (09) ◽  
pp. 1850018
Author(s):  
Marzio Cassandro ◽  
Immacolata Merola ◽  
Errico Presutti
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Renewal Process ◽  
Infinite Sequence ◽  
Mean Field ◽  
Coarse Graining ◽  
Inverse Temperature ◽  
Scaling Parameter ◽  
Kac Potentials ◽  
The Mean

We consider the [Formula: see text] Ising model with Kac potentials at inverse temperature [Formula: see text] where the mean field predicts a phase transition with two possible equilibrium magnetizations [Formula: see text], [Formula: see text]. We show that when the Kac scaling parameter [Formula: see text] is sufficiently small, typical spin configurations are described (via a coarse graining) by an infinite sequence of successive plus and minus intervals where the empirical magnetization is “close” to [Formula: see text], and respectively, [Formula: see text]. We prove that the corresponding marginal of the unique DLR measure is a renewal process.

Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics

Nonlinearity ◽  
1994 ◽  
Vol 7 (3) ◽  
pp. 633-696 ◽  
Author(s):  
A De Masi ◽  
E Orlandi ◽  
E Presutti ◽  
L Triolo
Keyword(s):  
Interface Dynamics ◽  
Kac Potentials

Corrections to the critical temperature in 2D Ising systems with Kac potentials

1995 ◽  
Vol 78 (3-4) ◽  
pp. 1131-1138 ◽  
Author(s):  
M. Cassandro ◽  
R. Marra ◽  
E. Presutti
Keyword(s):  
Critical Temperature ◽  
Kac Potentials ◽  
Ising Systems

Surface tension in Ising systems with Kac potentials

1996 ◽  
Vol 82 (3-4) ◽  
pp. 743-796 ◽  
Author(s):  
G. Alberti ◽  
G. Bellettini ◽  
M. Cassandro ◽  
E. Presutti
Keyword(s):  
Surface Tension ◽  
Kac Potentials ◽  
Ising Systems
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