| EPSRC Reference: |
GR/L15357/01 |
| Title: |
FUNCTIONAL INTEGRALS AND THE PLANAR ISING MODEL |
| Principal Investigator: |
Abraham, Professor D |
| Other Investigators: |
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| Department: |
Oxford Physics |
| Organisation: |
University of Oxford |
| Scheme: |
Overseas Travel Grants Pre-FEC |
| Starts: |
13 March 1996 |
Ends: |
12 August 1996 |
Value (£): |
6,165
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Summary on Grant Application Form |
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Novel methods are proposed for calculating the spontaneous magnetisation in the planar Ising model as an alternative to the Szego-Kac theorem Toplitz determinants, and for establishing path integral and summation methods rigorously for interfaces ad correlation functions. These methods use the transfer matrix and its diagonalisation using Jordan Wigner fermions and the Bogoliubov Valatin transformation. The pair correlation function is extracted by evaluating a special case of a Fedholm type and the spontaneous magnetisation is extracted by evaluating a special case of a Fredholm determinant. The 2-particle state gives the large-separation asympotics of the truncated pair function. By means of a careful definition of a position representation associated with the standard Bogoliubov-Valatin transformation, a path formulation can be derived with precisely specified errors the consequence of which will be assessed.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |