In this paper, we study phase transitions in asymmetrical fermion superfluids. In this scenario, the candidates to form pair are particles with mismatched masses and chemical potentials. We derive an expression for the critical temperature in terms of the gap and masses (or chemical potentials) when the constraint of equal Fermi surfaces m a µ a = m b µ b is imposed. *

In this work, we show that, due to the alternating orientation of the spins in the ground state of the artificial square spin ice, the influence of a set of spins at a certain distance of a reference spin decreases faster than the expected result for the long range dipolar interaction, justifying the use of the nearest neighbor two dimensional square spin ice model [1] as an effective model. Using an extension of the model presented in ref.[1], considering the influence of the eight nearest neighbors of each spin on the lattice, we analyze the thermodynamics of the model and study the monopoles and string densities dependence as a function of the temperature.

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an ansatz in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli-Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.

We propose a classical continuous model Hamiltonian with a ground state presenting a spin ice structure. We analyze the introduction of metastable excitations on this ground state, showing the emergence of pairs of magnetic monopoles. The interaction between monopoles and dipoles in the system is studied. As a consequence, we obtain an effective nonlocal interaction between monopoles and dipoles from a local classical spin model. *