  The swap Monte Carlo algorithm combines the translational motion with the
exchange of particle species, and is unprecedentedly efficient for some models
of glass former. In order to clarify the physics underlying this acceleration,
we study the problem within the mean field replica liquid theory. We extend the
Gaussian ansatz so as to take into account the exchange of particles of
different species, and we calculate analytically the dynamical transition
points corresponding to the swap and standard Monte Carlo algorithms. We show
that the system evolved with the standard Monte Carlo algorithm exhibits the
dynamical transition before that of the swap Monte Carlo algorithm. We also
test the result by performing numerical simulations of a binary mixture of the
Mari-Kurchan model, both with standard and swap Monte Carlo. This scenario
provides a possible explanation for the efficiency of the swap Monte Carlo
algorithm. Finally, we discuss how the thermodynamic theory of the glass
transition should be modified based on our results.
