Ramsey theory of the phase transitions of the second order

Abstract

The Ramsey theory-based approach to the phase transitions of the second order is suggested. The phase transitions of the second order are seen as the switching of physical interactions\(/\)chemical bonds between the entities forming the primitive cell of the material. Such a switching is typical for phase change materials. The phase transition of the second order takes place if the energy of the primitive cell is kept constant by changing the spatial order of the chemical bonds. The breaking of the initial symmetry of the cell accompanies the switching of interactions between the entities forming the primitive cell. The order parameter\(/\)the degree of ordering characterising the ordering within the primitive cell is re-defined. The introduced degree of ordering quantifies the ordering of links\(/\)interactions\(/\)chemical bonds between entities constituting the 2D lattice, whereas, the classical ‘Landau degree of order’ quantifies the symmetry breaking under variation in spatial locations of these entities. The suggested approach is generalised easily for 3D primitive cells. The thermal capacity of the non-symmetrical phase is larger than that of the symmetrical phase. For the primitive cells consisting of six interacting entities, the Ramsey theory predicts the inevitable appearance of unstable monochromatic triangles, when the links correspond to attraction or repulsion interactions. The situation becomes different for the primitive cells of five interacting entities.