Corso di laurea magistrale Interateneo in Fisica dei sistemi complessi

Speaker: Andrea Cavagna (ISC, Roma)

I will sketch the general mechanism of spontaneous symmetry breaking in the continuous case in statistical field theory, with a particular emphasis on the role of longitudinal vs transverse modes. I will schematically illustrate how massless Goldstone modes emerge and why they prescribe that the transverse susceptibility must diverge, and how this is related to the Mermin-Wagner theorem regulating the lower critical dimension in the continuous case. I will discuss the subtle yet crucial coupling between longitudinal and transverse modes, leading to the weaker divergence of the longitudinal susceptibility. All these concepts, which are standard tools in statistical field theory, will be crucial in understanding the relevance of scale-free correlations in certain biological systems characterized by broken continuous symmetries.