  In traditional thermodynamics, temperature is a local quantity: a subsystem
of a large thermal system is in a thermal state at the same temperature as the
original system. For strongly interacting systems, however, the locality of
temperature breaks down. We study the possibility of associating an effective
thermal state to subsystems of infinite chains of interacting spin particles of
arbitrary finite dimension. We study the effect of correlations and criticality
in the definition of this effective thermal state and discuss the possible
implications for the classical simulation of thermal quantum systems.
