The discrete Gaussian chain with 1/r
n interactions: Exact results |
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Authors: | K H Kjaer H J Hilhorst |
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Institution: | (1) Laboratorium voor Technische Natuurkunde, Postbus 5046, 2600 GA Delft, The Netherlands |
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Abstract: | We show that the discrete Gaussian chain with interactionV(r) = 1/(r
2–1/4) is self-dual. At the dual temperaturek
B
T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent . We also consider interactionsV(r)–1/r
n and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark. |
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Keywords: | Discrete Gaussian model long-range interactions self-duality |
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