Finite size scaling study of lattice models in the three-dimensional Ising universality class

By M. Hasenbusch. 2010

251 citations recorded by the source corpus.

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates for critical exponents. We focus on values of D, where the amplitudes of leading corrections are small. Furthermore we employ improved observables that have a small amplitude of the leading correction. We obtain nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with those obtained from previous Monte Carlo simulations and high temperature series expansions of lattice models, by using field theoretic methods and experiments.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6faf3ec72ed61e2623aacec12a0fbfb8bf140d4c

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In Condensed Matter Physics

1. David Simmons-Duffin
2. S. Rychkov
3. David Poland
4. A. Eichhorn
5. A. Vichi
6. F. Gliozzi
7. Antonio Rago
8. M. Meineri

In Mathematical Physics

1. David Simmons-Duffin
2. David Poland
3. S. Rychkov
4. A. Eichhorn
5. S. El-Showk
6. M. Paulos
7. L. Canet
8. W. Metzner

In Statistical and Nonlinear Physics

1. S. Rychkov
2. David Poland
3. Filip Kos
4. A. Eichhorn
5. David Simmons-Duffin
6. A. Vichi
7. L. Canet
8. F. Gliozzi

Citations in the corpus

• Minimally subtracted six loop renormalization of $O(n)$-symmetric $\phi^4$ theory and critical exponents (2017, methodology): “Theoretical predictions are more accurate, like the Monte Carlo simulations [78] with η = 0.”
• Boundary and interface CFTs from the conformal bootstrap (2015, background): “The critical indices η and ν for N = 0, 1, 2, 3 are taken respectively from references [42], [43], [44] and [45].”
• The nonperturbative functional renormalization group and its applications (2020, result): “Table 3: Critical exponents of Model A in d = 3 from the different FRG approximations (LPA, LPA′ [408] and DE2 withouta or withb frequency regularization [404]), compared with results from other field theoretical methods (FT) [14, 409] and Monte Carlo simulations (MC) [123, 410, 411].”
• A semidefinite program solver for the conformal bootstrap (2015, methodology): “With SDPB , we have significantly improved the precision of (∆ σ , ∆ ǫ ) in the 3d Ising CFT.”
• Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, background): “Acknowledgments We are grateful to M. Hasenbusch, M. Henkel, D. Mouhanna and E. Vicari for the useful communications concerning their work.”
• Bootstrapping mixed correlators in the 3D Ising model (2014, methodology): “4127(11), in agreement with the most precise Monte-Carlo simulations [39], and also the c-minimization conjecture of [23].”