The virial expansion, in statistical mechanics, makes use of the sums of the Mayer weight of all 2-connected graphs on n vertices. We study the Second Mayer weight ωM(c) and the Ree-Hoover weight ωRH(c) of a 2-conne...The virial expansion, in statistical mechanics, makes use of the sums of the Mayer weight of all 2-connected graphs on n vertices. We study the Second Mayer weight ωM(c) and the Ree-Hoover weight ωRH(c) of a 2-connected graph c which arise from the hard-core continuum gas in one dimension. These weights are computed using signed volumes of convex polytopes naturally associated with the graph c. In the present work, we use the method of graph homomorphisms, to give new formulas of Mayer and Ree-Hoover weights for special infinite families of 2-connected graphs.展开更多
We study graph weights which naturally occur in Mayer’s theory and Ree-Hoover’s theory for the virial expansion in the context of an imperfect gas. We pay particular attention to the Mayer weight and Ree-Hoover weig...We study graph weights which naturally occur in Mayer’s theory and Ree-Hoover’s theory for the virial expansion in the context of an imperfect gas. We pay particular attention to the Mayer weight and Ree-Hoover weight of a 2-connected graph in the case of the hard-core continuum gas in one dimension. These weights are calculated from signed volumes of convex polytopes associated with the graph. In the present paper, we use the method of graph homomorphisms, to develop other explicit formulas of Mayer weights and Ree-Hoover weights for infinite families of 2-connected graphs.展开更多
文摘The virial expansion, in statistical mechanics, makes use of the sums of the Mayer weight of all 2-connected graphs on n vertices. We study the Second Mayer weight ωM(c) and the Ree-Hoover weight ωRH(c) of a 2-connected graph c which arise from the hard-core continuum gas in one dimension. These weights are computed using signed volumes of convex polytopes naturally associated with the graph c. In the present work, we use the method of graph homomorphisms, to give new formulas of Mayer and Ree-Hoover weights for special infinite families of 2-connected graphs.
文摘We study graph weights which naturally occur in Mayer’s theory and Ree-Hoover’s theory for the virial expansion in the context of an imperfect gas. We pay particular attention to the Mayer weight and Ree-Hoover weight of a 2-connected graph in the case of the hard-core continuum gas in one dimension. These weights are calculated from signed volumes of convex polytopes associated with the graph. In the present paper, we use the method of graph homomorphisms, to develop other explicit formulas of Mayer weights and Ree-Hoover weights for infinite families of 2-connected graphs.
