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Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2026, Tutor: Jordi Salvadó Serra

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The potentials derived from the Non-Relativistic limit of Quantum Field Theory providea direct connection between microscopic fundamental interactions and macroscopic behaviour.
By incorporating the potential into a classical Hamiltonian, we study the system using Monte Carlomethods based on the Metropolis algorithm. Interactions mediated by a pseudo-scalar particlegive rise to a spin-dependent potential. In a one-dimensional system, we obtain the thermal equilibriumconfigurations that emerge in ordered phases characterized by anti-aligned spin patternsalong a preferred axis and a temperature-driven phase transition, marked by a susceptibility peak
at T · m2/g2 = 1.75 · 104MeV3. In contrast, in a two-dimensional system, the equilibrium configurationshows mass-dependent differences. These results bridge microscopic particle physics withemergent collective behaviour, offering insights into thermodynamic phases in systems with exoticspin-dependent forces.