# An ab initio Calculation of the Universal Equation of State for the ON Model - Condensed Matter > Statistical Mechanics

An ab initio Calculation of the Universal Equation of State for the ON Model - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Using an Environmentally Friendly Renormalization Group we derive an abinitio universal scaling form for the equation of state for the ON model,y=fx, that exhibits all required analyticity properties in the limits $x\to0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on aphenomenological scaling ansatz the scaling function is derived solely from theunderlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the threeWilson functions $\gamma \lambda$, $\gamma \phi$ and $\gamma {\phi^2}$ whichexhibit a non-trivial crossover between the Wilson-Fisher fixed point and thestrong coupling fixed point associated with the Goldstone modes on thecoexistence curve. We give explicit results for N=2, 3 and 4 to one-loop orderand compare with known results.

Author: Denjoe O'Connor, J.A. Santiago, C.R. Stephens

Source: https://arxiv.org/