کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10720782 | 1031509 | 2013 | 41 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A generalized Beraha conjecture for non-planar graphs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study the partition function ZG(nk,k)(Q,v) of the Q-state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1⩽k⩽7. We also consider two specializations of ZG(nk,k), namely the chromatic polynomial PG(nk,k)(Q) (corresponding to v=â1), and the flow polynomial ΦG(nk,k)(Q) (corresponding to v=âQ). In these two cases, we study their zeros in the complex Q-plane for 1⩽k⩽7. We pay special attention to the accumulation loci of the corresponding zeros when nââ. We observe that the Berker-Kadanoff phase that is present in two-dimensional Potts models, also exists for non-planar recursive graphs. Their qualitative features are the same; but the main difference is that the role played by the Beraha numbers for planar graphs is now played by the non-negative integers for non-planar graphs. At these integer values of Q, there are massive eigenvalue cancellations, in the same way as the eigenvalue cancellations that happen at the Beraha numbers for planar graphs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nuclear Physics B - Volume 875, Issue 3, 21 October 2013, Pages 678-718
Journal: Nuclear Physics B - Volume 875, Issue 3, 21 October 2013, Pages 678-718
نویسندگان
Jesper Lykke Jacobsen, Jesús Salas,