Directed polymer inside a parabola: Exact solution

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Abstract

We consider a directed polymer on a square lattice confined inside a parabola with boundaries Y=Cx. Generalizing standard transfer-matrix methods, an effective transfer operator was introduced that takes into account slow variation of the size of the system in the y direction. By an exact calculation the effect of the confinement is found to be relevant and irrelevant for 1/2, respectively; in the former case the thermodynamical functions have a stretched-exponential behavior around the critical point. For =1/2 the geometrical constraint is marginal, and the critical exponents are nonuniversal.

Original languageEnglish
Pages (from-to)7024-7029
Number of pages6
JournalPhysical Review A
Volume45
Issue number10
DOIs
Publication statusPublished - 1992

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parabolas
polymers
matrix methods
critical point
exponents
operators

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Directed polymer inside a parabola : Exact solution. / Iglói, F.

In: Physical Review A, Vol. 45, No. 10, 1992, p. 7024-7029.

Research output: Contribution to journalArticle

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