Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Flat Phase of Crystalline Membranes   We present the results of a high-statistics Monte Carlo simulation of a
phantom crystalline (fixed-connectivity) membrane with free boundary. We verify
the existence of a flat phase by examining lattices of size up to $128^2$. The
Hamiltonian of the model is the sum of a simple spring pair potential, with no
hard-core repulsion, and bending energy. The only free parameter is the the
bending rigidity $\kappa$. In-plane elastic constants are not explicitly
introduced. We obtain the remarkable result that this simple model dynamically
generates the elastic constants required to stabilise the flat phase. We
present measurements of the size (Flory) exponent $\nu$ and the roughness
exponent $\zeta$. We also determine the critical exponents $\eta$ and $\eta_u$
describing the scale dependence of the bending rigidity ($\kappa(q) \sim
q^{-\eta}$) and the induced elastic constants ($\lambda(q) \sim \mu(q) \sim
q^{\eta_u}$). At bending rigidity $\kappa = 1.1$, we find $\nu = 0.95(5)$
(Hausdorff dimension $d_H = 2/\nu = 2.1(1)$), $\zeta = 0.64(2)$ and $\eta_u =
0.50(1)$. These results are consistent with the scaling relation $\zeta =
(2+\eta_u)/4$. The additional scaling relation $\eta = 2(1-\zeta)$ implies
$\eta = 0.72(4)$. A direct measurement of $\eta$ from the power-law decay of
the normal-normal correlation function yields $\eta \approx 0.6$ on the $128^2$
lattice.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio