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- W2258315992 abstract "We present some promising ideas to treat the problem of making completely rigorous the development of our expression for $lambda_d(p)$ of the monomer-dimer problem on a $d$-dimensional hypercubic lattice begin{equation}label{abstract1} lambda_d(p)=frac{1}{2}Big(pln(2d)-pln(p)-2(1-p)ln(1-p)-pBig) +sum_{k=2}a_k(d)p^k end{equation} where $a_k(d)$ is a sum of powers $(1/d)^r$ for begin{equation}label{abstract2} k-1leq rleq k/2 end{equation} In fact as we will point out one has allready rigorously established the convergence of the sum in expression for $lambda$ for small $p$. It is the $d$ dependence of $a_k(d)$ that has yet to be rigorously shown. We do not now know how to complete the proof." @default.
- W2258315992 created "2016-06-24" @default.
- W2258315992 creator A5037302391 @default.
- W2258315992 date "2015-09-13" @default.
- W2258315992 modified "2023-09-27" @default.
- W2258315992 title "Proof of Convergence for the Lattice Monomer-Dimer Cluster Expansion I, a Simplified Model" @default.
- W2258315992 cites W1629714101 @default.
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- W2258315992 hasPublicationYear "2015" @default.
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