کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903727 | 1632914 | 2018 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The free-fermionic C2(1) loop model, double dimers and Kashaev's recurrence
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The free-fermionic C2(1) loop model, double dimers and Kashaev's recurrence The free-fermionic C2(1) loop model, double dimers and Kashaev's recurrence](/preview/png/8903727.png)
چکیده انگلیسی
We study a two-color loop model known as the C2(1) loop model. We define a free-fermionic regime for this model, and show that under this assumption it can be transformed into a double dimer model. We then compute its free energy on periodic planar graphs. We also study the star-triangle relation or Yang-Baxter equations of this model, and show that after a proper parametrization they can be summed up into a single relation known as Kashaev's relation. This is enough to identify the solution of Kashaev's relation as the partition function of a C2(1) loop model with some boundary conditions, thus solving an open question of Kenyon and Pemantle [29] about the combinatorics of Kashaev's relation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 158, August 2018, Pages 407-448
Journal: Journal of Combinatorial Theory, Series A - Volume 158, August 2018, Pages 407-448
نویسندگان
Paul Melotti,