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The combination of theory and simulation is necessary in the investigation of properties of complex systems where each method alone cannot do the task properly. Theory needs simulation to test ideas and to check approximations. Simulation needs theory for modeling and for understanding results coming out from computers. In this review, we give recent examples to illustrate this necessary combination in a few domains of interest such as frustrated spin systems, surface magnetism, spin transport and melting. Frustrated spin systems have been intensively studied for more than 30 years. Surface effects in magnetic materials have been widely investigated also in the last three decades. These fields are closely related to each other and their spectacular development is due to numerous applications. We confine ourselves to theoretical developments and numerical simulations on these subjects with emphasis on spectacular effects occurring at frontiers of different phases.
The task of accurately locating fluid phase boundaries by means of computer simulation is hampered by problems associated with sampling both coexisting phases in a single simulation run. We explain the physical background to these problems and descri
We have used the Monte Carlo (MC) simulation method with Metropolis algorithm to study the finite temperature phase transition properties of a binary alloy spherical nanoparticle with radius $r$ of the type $A_{p}B_{1-p}$. The system consists of two
Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase I, a phase characterized by a change from out
We simulate the motion of spherical particles in a phase-separating binary mixture. By combining cell dynamical equations with Langevin dynamics for particles, we show that the addition of hard particles significantly changes both the speed and the m
We introduce the Loschmidt amplitude as a powerful tool to perform spectroscopy of generic many-body wave functions and use it to interrogate the wave function obtained after ramping the transverse field quantum Ising model through its quantum critic