A Finite-Lattice Model from a Reciprocal Cost Action: Spectral and Reflection-Positivity Properties (opens in new tab)

We study the finite-lattice statistical-mechanical model whose nearest-neighbor bond potential is the reciprocal cost $J(e^\varepsilon)=\cosh\varepsilon-1$, selected by the d'Alembert functional equation under the stated regularity and calibration assumptions. The structural inputs are stated explicitly; once they are fixed, the analysis is rigorous mathematics about the bond action $V(\Delta\phi)=\cosh(\Delta\phi)-1$ on finite boxes in $\mathbb...