Combinatorics and physics ice-type model is six vertex model with domain wall boundary conditions. Combinatorics and physics Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics. "Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory.". "Physical combinatorics might be defined naively as combinatorics guided by ideas or insights from physics". Combinatorics has always played an important role in quantum field theory and statistical physics. However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer, showing that the renormalization
History of variational principles in physics History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a function or functional. This article describes the historical development of such principles. Variational principles are found among earlier ideas in surveying and optics. The rope stretchers of ancient Egypt stretched corded ropes between two points to measure the path which minimized the distance of separation, and Claudius Ptolemy, in his Geographia (Bk 1, Ch 2), emphasized that one must correct for "deviations