  The temperature induced phase transition is investigated in the one-component
scalar field \phi^4 model on a lattice by using Monte Carlo simulations. Using
the GPGPU technology a huge amount of data is collected that gives a
possibility to determine the Linde-Weinberg low bound on the coupling constant
\lambda_0 and investigate the type of the phase transition for a wide interval
of coupling values. It is found that for the values of \lambda close to this
bound a weak-first-order phase transition happens. It converts into a second
order phase transition with the increase of \lambda. A comparison with analytic
calculations in continuum field theory and lattice simulations obtained by
other authors is given.
