Graphical representations and worm algorithms for the O(N) spin model
Communications in Theoretical Physics, ISSN: 0253-6102, Vol: 75, Issue: 11
2023
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Article Description
We present a family of graphical representations for the O(N) spin model, where N ≥ 1 represents the spin dimension, and N = 1, 2, 3 corresponds to the Ising, XY and Heisenberg models, respectively. With an integer parameter 0 ≤ ℓ ≤ N/2, each configuration is the coupling of ℓ copies of subgraphs consisting of directed flows and N − 2ℓ copies of subgraphs constructed by undirected loops, which we call the XY and Ising subgraphs, respectively. On each lattice site, the XY subgraphs satisfy the Kirchhoff flow-conservation law and the Ising subgraphs obey the Eulerian bond condition. Then, we formulate worm-type algorithms and simulate the O(N) model on the simple-cubic lattice for N from 2 to 6 at all possible ℓ. It is observed that the worm algorithm has much higher efficiency than the Metropolis method, and, for a given N, the efficiency is an increasing function of ℓ. Besides Monte Carlo simulations, we expect that these graphical representations would provide a convenient basis for the study of the O(N) spin model by other state-of-the-art methods like the tensor network renormalization.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85177597804&origin=inward; http://dx.doi.org/10.1088/1572-9494/acfbdf; https://iopscience.iop.org/article/10.1088/1572-9494/acfbdf; http://sciencechina.cn/gw.jsp?action=cited_outline.jsp&type=1&id=7681171&internal_id=7681171&from=elsevier; https://dx.doi.org/10.1088/1572-9494/acfbdf; https://validate.perfdrive.com/9730847aceed30627ebd520e46ee70b2/?ssa=8a4f3ccc-893d-4572-8201-d57c0668b35e&ssb=30462218579&ssc=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F1572-9494%2Facfbdf&ssi=bda890fe-cnvj-4221-92bc-a7258a36f58f&ssk=botmanager_support@radware.com&ssm=8910350736874348157432417697290676&ssn=b9e94f4ef853d4ab38f9710ba6ec23e0456edf9f3776-e6a8-45b6-a6a2c4&sso=df7f8892-40540c8f09fabfaa9c2199375404badaae4484b27ba6ee3b&ssp=21416645781725059717172525525776185&ssq=99872447640783868642190140059283482973634&ssr=NTIuMy4yMTcuMjU0&sst=com.plumanalytics&ssu=&ssv=&ssw=&ssx=eyJ1em14IjoiN2Y5MDAwMjQ4NjExMzgtYzM4Mi00NGU1LTk0ODYtNzAxNTllMDI4YTFkMy0xNzI1MDkwMTQwOTk2MTg2MjY2MTg0LWVmZTI0OTRmZTZmOGVjMjI1NzQzIiwiX191em1mIjoiN2Y2MDAwZWJkM2NhNTItNzg4OC00N2U1LWFjN2MtMDAwNDMwZWVlNDMyMTcyNTA5MDE0MDk5NjE4NjI2NjE4NC1jYWE0YWY2NmRmZGM5NjZmNTc0MyIsInJkIjoiaW9wLm9yZyJ9
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