Exact solution of asymmetric gelation between three walks on the square lattice
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908534366535680 |
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| author | Owczarek, Aleksander L Rechnitzer, Andrew |
| author_facet | Owczarek, Aleksander L Rechnitzer, Andrew |
| contents | We find and analyse the exact solution of a model of three different
polymers with asymmetric contact interactions in two dimensions, modelling a
scenario where there are different types of polymers involved. In particular, we find
the generating function of three directed osculating walks in star
configurations on the square lattice with two interaction Boltzmann weights,
so that there is one type of contact interaction between the top pair of walks and a
different interaction between the bottom pair of walks. These osculating
stars are found to be the most amenable to exact solution using functional
equation techniques in comparison to the symmetric case where three friendly
walks in watermelon configurations were successfully solved with the same
techniques. We elucidate the phase diagram, which has four phases, and find
the order of all the phase transitions between them. We also calculate the
entropic exponents in each phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solution of asymmetric gelation between three walks on the square lattice Owczarek, Aleksander L Rechnitzer, Andrew Statistical Mechanics Mathematical Physics Combinatorics We find and analyse the exact solution of a model of three different polymers with asymmetric contact interactions in two dimensions, modelling a scenario where there are different types of polymers involved. In particular, we find the generating function of three directed osculating walks in star configurations on the square lattice with two interaction Boltzmann weights, so that there is one type of contact interaction between the top pair of walks and a different interaction between the bottom pair of walks. These osculating stars are found to be the most amenable to exact solution using functional equation techniques in comparison to the symmetric case where three friendly walks in watermelon configurations were successfully solved with the same techniques. We elucidate the phase diagram, which has four phases, and find the order of all the phase transitions between them. We also calculate the entropic exponents in each phase. |
| title | Exact solution of asymmetric gelation between three walks on the square lattice |
| topic | Statistical Mechanics Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2507.17111 |