Spontaneous Symmetry Breaking in Finite Systems

The orthodox characterisation of spontaneous symmetry breaking (SSB) in statistical mechanics appeals to novel properties of systems with infinite degrees of freedom, namely the existence of multiple equilibrium states. This raises the same puzzles about the status of the thermodynamic limit fueling recent debates about phase transitions. I argue here that there are prospects of explaining the success of the standard approach to SSB in terms of the properties of large finite systems and consequently, despite initial appearances, the need to account for SSB phenomena does not offer decisive support to claims about the explanatory and representational indispensability of the thermodynamic limit.