Alessio	Turchi	Università di Firenze	#	
Dynamics and equilibrium properties of β-HMF long range 
model
#	
Long range interacting systems have been found to possess unique 
equilibrium and out-of-equilibrium features, but still now 
there are only a few applications to real physical systems. 
The new  β-HMF model we propose here is a modification of 
the 
well known HMF toy-model by adding a continuous range 
parameter, thus trying to extend its applicability. This model 
has a completely different dynamic and shows interesting 
self-organization properties. At equilibrium it 
self-consistently defines a crystal lattice at low energies 
and shows multiple phase transitions between different 
thermodynamical states characterized by different structures. 
Even if the dynamics of the model are completely different 
from the HMF we were able to recover many features from that 
model. We were able to solve the model analytically for finite 
sizes and obtain the equilibrium distribution function. 
Results show that the HMF magnetization transition curve is 
perfectly reproduced for a wide range of parameters, thus 
showing thermodynamical equivalence to the HMF.