Physical Aspects of 2014 Nobel Prize in Physiology or Medicine: 2. The First Principle and Universality Class for Grid Cells in the Brain

Abstract

The main purpose of this review article is to use the fluctuation theory of phase transitions for studying the process of the emergence of hexagonal grid cells in the brain (2014 Nobel Prize in Physiology or Medicine). Particular attention is paid to the application of the Feynman’s classification of three stages of the study of natural phenomena for: 1) a brief description of the experimental stage of the discovery of the hexagonal structures of grid cells in human and animal brains; 2) the theoretical stage of research on the hexagon formation in the physical system of Benard cells, as well as the neurophysiological system of grid cells, discovered by Edward Mozer and May-Britt Mozer; 3) the most important stage, which allows one to formulate the first principle of the emergence of grid cells in the brain and, generally speaking, the first principle for the hexagon formation in different objects of inanimate and living nature. Our original theoretical findings are the following: (a) Polyakov’s conformal invariance hypothesis is violated for a system of grid cells in the brain; (b) the system of grid cells in the brain belongs to the universality class including the 3D Ising model in a magnetic field, as well as a real classical liquid-vapor system;(c) to formulate the first principle for a reliable theoretical justification of the emergence of hexagonal grid cells in the brain, it is necessary to use the fluctuating part of Gibbs thermodynamic potential (the Ginzburg–Landau Hamiltonian) for a system with chemical (biochemical) reactions.