  Sine-square deformation (SSD) is a treatment proposed in quantum systems,
which spatially modifies a Hamiltonian, gradually decreasing the local energy
scale from the center of the system toward the edges by a sine-squared envelope
function. It is known to serve as a good boundary condition as well as to
provide physical quantities reproducing those of the infinite-size systems. We
apply the SSD to one- and two-dimensional classical Ising models. Based on the
analytical calculations and Monte Carlo simulations, we find that the classical
SSD system is regarded as an extended canonical ensemble of a local subsystem
each characterized by its own effective temperature. This effective temperature
is defined by normalizing the system temperature by the deformed local energy
scale. A single calculation for a fixed system temperature provides a set of
physical quantities of various temperatures that quantitatively reproduce well
those of the uniform system.

Strongly Correlated Electrons;Statistical Mechanics