Journal
PHYSICAL REVIEW LETTERS
Volume 121, Issue 18, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.121.185701
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Funding
- Australian Research Council [DP140100559]
- Australian Government
- Monash eResearch Centre
- Monash University
- Australian Mathematical Society
- National Key R&D Program of China [2016YFA0301604]
- National Natural Science Foundation of China [11625522]
- eSolutions-Research Support Services through the use of the MonARCH HPC Cluster
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We address a long-standing debate regarding the finite-size scaling (FSS) of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rigorously. We prove that this model exhibits the same universal FSS behavior previously conjectured for the self-avoiding walk and Ising model on finite boxes in high-dimensional lattices. Our results show that the mean walk length of the random walk model controls the scaling behavior of the corresponding Green's function. We numerically demonstrate the universality of our rigorous findings by extensive Monte Carlo simulations of the Ising model and self-avoiding walk on five-dimensional hypercubic lattices with free and periodic boundaries.
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