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\begin{document}

\title{Critical scaling to infinite temperature}


\author{I. A.~Campbell}
\affiliation{Laboratoire des Collo\"ides, Verres et Nanomat\'eriaux,
  Universit\'e Montpellier II, 34095 Montpellier, France}



\begin{abstract}
Three dimensional Ising model ferromagnets on different lattices with near neighbor interactions and on simple cubic lattices with equivalent interactions out to further neighbors are studied numerically. With an appropriate choice of scaling variable and scaling expression the susceptibility data are analysed using the critical Renormalization Group Theory formalism over the entire temperature range above $T_c$. Experimental data on a metallic ferromagnet (Ni) and a fluid (Xe) are interpreted in the same manner to estimate effective interaction ranges.


\end{abstract}

\pacs{ 75.50.Lk, 05.50.+q, 64.60.Cn, 75.40.Cx}

\maketitle

In the very extensive studies which have been devoted to critical phenomena attention has understandably been mainly concentrated on the regime in the immediate neighborhood of the critical point; data are analysed using the leading terms in the Renormalization Group Theory (RGT) formalism. It is widely considered that as correction terms proliferate outside this narrow "critical region" they lead ultimately to a crossover towards Gaussian fixed point mean-field-like behavior above a temperature $T_g$ determined (at dimensions below the upper critical dimension) by the Ginzburg criterion \cite{ginzburg:60}. This criterion expresses the breakdown of a high temperature Landau regime due to critical fluctuations.




The susceptibility results for various lattice sizes $L$ are exhibited in Figure 1 in the form of plots of $\chi(\tau)\tau^{\gamma}$ against $\tau^{\theta}$.

\begin{figure}
  \includegraphics[width=3.5in]{highT_fig1}
\caption{(Color online) The normalized reduced susceptibility $\chi(\tau)\tau^{\gamma}$ as a function of $\tau^{\theta}$ for the diamond, sc, bcc, fcc, $z18, z26, z32$ and $z56$ sc Ising models, top to bottom (black, red, green, blue, cyan, pink, yellow, olive). The exponents are taken to be $\gamma = 1.2371$ and $\theta =0.50$.   }
  \protect\label{fig:1}
\end{figure}
\begin{table}[htbp]
  \caption{\label{Table:I} Values of the fitting parameters for $\chi(\tau)$ in each of the models, as defined in Eqn. \ref{chitau}.}
  \begin{ruledtabular}
\begin{tabular}{cccccc}

$z$&$\beta_c$&$C_{\chi}$&$a_{\chi}$&$k_{\chi}$&$\lambda_{\chi}$ \\
$4$&$0.3697$&$1.245$&$-0.1382$&$-0.059$&$2$\\
$6$&$0.221655$&$1.116$&$-0.0914$&$-0.0125$&$3$\\
$8$&$0.15737$&$1.032$&$-0.039$&$0.008$&$1.15$\\
$12$&$0.102067$&$1.022$&$-0.062$&$0.04$&$1.5$ \\
$18$&$0.06442$&$0.871$&$0.111$&$0.038$&$0.9$\\
$26$&$0.0430385$&$0.765$&$0.302$&$0.009$&$1$\\
$32$&$0.0343267$&$0.703$&$0.428$&$-0.006$&$3$\\
$56$&$0.0189291$&$0.575$&$0.800$&$-0.06$&$1.5$\\
\end{tabular}
\end{ruledtabular}
\end{table}


\begin{thebibliography}{99}

\bibitem{ginzburg:60} V. L. Ginzburg, Fiz. Tverd. Tela (Leningrad){\bf 2}, 2031 (1960)(Sov. Phys. Solid State {\bf 2}, 1824 (1960)).

\end{thebibliography}{99}

\end{document}