Condensed Matter Physics, 2007, vol. 10, No. 2(50), p. 173178, English

Title: The effect of finite size of the system on correlation length behaviour at the presence of external field
  M.P.Kozlovskii (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine)

The explicit analytical expression for the effective correlation length ξ as a function of reduced temperature τ, external field h and system size L for the Ising-like system near the phase transition point Tc is obtained. The role of these quantities in the formation of the correlation length value is ascertained. It is shown that the irregular increase of the correlation length exists only in the case of τ → 0, h → 0 and L → ∞. With deviation from these values the essential slowing down exists for the increasing\xi. The criterium of the permissible range of temperature values (field values), where the correlation length behaviour is defined by temperature (or field) variable, is established for the fixed size of the system. Beyond this range τ<τc, hcr the system size becomes crucial for forming the correlation length.

Key words: phase transition, correlation length, external field, finite size system
PACS: 05.50.+q, 64.60.Fr, 75.10.Hk

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