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Book cover Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics

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Abstract

Our understanding of nature is built on the precise knowledge of the interaction between distinct constituents of matter.

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Notes

  1. 1.

    Note that there are continuous phase transitions that do not break any symmetry, as it is the case of the Kosterlitz–Thouless phase transition [13]. However, this special type of phase transition is not covered in this thesis.

  2. 2.

    For temperature, for example, this parameter would become \(\epsilon =T/T_c-1\) where \(T_c\) stands for the critical temperature of the phase transition.

  3. 3.

    There is in principle no underlying reason to assume that these exponents take the same value at both sides of the critical point, however, the inspection of phase transitions in most systems teaches us that this is actually the case. Nevertheless, since \(m= 0\) in the disordered phase, it is evident that \(\beta \) is, by definition, an exception. It is worth mentioning however that there are special situations where \(\kappa _{+}\ne \kappa _{-}\).

  4. 4.

    Note that an anti-ferromagnetic Ising model with zero external field can be mapped onto its ferromagnetic counterpart by redefining spin variables as \(\tilde{\sigma }_i=(-1)^i\sigma _i\).

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    Ricardo Puebla

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Puebla, R. (2018). Introduction. In: Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-00653-2_1

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