  Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted
by Mermin-Wagner theorem at any finite temperature in presence of short-range
exchange interaction.Kosterlitz and Thouless using XY spin model showed that
how an order state could developed in 2D spin system in presence of short range
isotropic interaction.Very recent discovery of several van der waals magnet
revised and redefined our understanding on 2D Heisenberg magnet and its ground
state properties.After a rigorous and careful study of several 2D magnetic
material we have realized from both experimentally and numerically that the
finite size of a 2D system has great impact on the ground state symmetry
breaking.Because of that finite size effect more often an anisotropic residual
magnetic moment is generated and trigger the spontaneous symmetry breaking at
finite temperature(T) and even only presence of short-range interaction we
observed the phase transition of that Heisenberg spin system.In this present
work we have shown the basic role of finite size,anisotropy during the symmetry
breaking of 2D Heisenberg XY magnet.Here we have simulated Kosterlitz-Thouless
transition using classical Monte-carlo simulation and study the effect of
anisotropy during the phase transition.We presented the behaviour of different
thermodynamic properties of 2D XY spin model system during the
Kosterlitz-Thouless(KT) transition.The generic characteristic of KT transition
which make it distinct from other critical phenomena is that the peak of heat
capacity is not diverging with increase of system size rather peak is
decreasing with the increasing of system size near at transition
temperature.Here we are observing that behaviour in our present simulation and
that specific behaviour help us for classifying the present transition as
Kosterlitz-Thouless(KT) transition.
