Soft Matter and Complex Systems Seminar

I will review some approaches to describe second-order phase transitions (PhT) with the use of theory of singularities of maps (ST) (customarily although not quite correctly called 'catastrophe theory'). Most representative names here are Landau and Thom. The common opinion is that description of phase transitions by singularity theory is wrong as it gives mean-field critical exponents. I will argue that the programme: PhT vs ST has both right and wrong aspects. Moreover, I will conjecture that singularities of maps are still closely related to description of phase transitions and critical region - not immediately, but through Laplace integrals (or rather certain extensions of this notion).