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Phase Transition in Hyperbolic Space

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Percolation:
1512.05404: Jorge H. Lopez, J. M. Schwarz, "Constraint percolation on hyperbolic lattices"
1407.3454: Takehisa Hasegawa, Tomoaki Nogawa, Koji Nemoto, "Critical Phase in Complex Networks: a Numerical Study"
1111.5626: Hang Gu, Robert M. Ziff, "Crossing on hyperbolic lattices"
1004.2622: Seung Ki Baek, Petter Minnhagen, Beom Jun Kim, "Surface and bulk criticality in midpoint percolation"
1003.6012: Petter Minnhagen, Seung Ki Baek, "Exact Results for the Extended Binary Tree"
0910.5812: Tomoaki Nogawa, Takehisa Hasegawa, "Reply to Comment on `Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees'"
0910.4340: Seung Ki Baek, Petter Minnhagen, Beom Jun Kim, "Comment on `Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'"
0907.0938: Francois Sausset, Cristina Toninelli, Giulio Biroli, Gilles Tarjus, "Bootstrap percolation and kinetically constrained models on hyperbolic lattices"
0901.0483: Seung Ki Baek, Petter Minnhagen, Beom Jun Kim, "Percolation on hyperbolic lattices"
0810.1602: Tomoaki Nogawa, Takehisa Hasegawa, "Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees"
math/0410422: Assaf Naor, Yuval Peres, Oded Schramm, Scott Sheffield, "Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces"
math/9912233: Itai Benjamini, Oded Schramm, "Percolation in the Hyperbolic Plane"
9705.JSP: C. Chris Wu, "Continuity of percolation probability on hyperbolic graphs"

Ising Model (Potts, etc.):
1511.08358: Marcel Serina, Jozef Genzor, Yoju Lee, Andrej Gendiar, "Free Energy Analysis of Spin Models on Hyperbolic Lattice Geometries"
1408.0669: Vijay Singh, C. T. Brunson, Stefan Boettcher, "From Discontinuous to Infinite-Order Transitions on a Hyperbolic Network"
1403.6712: Dario Benedetti, "Critical behavior in spherical and hyperbolic spaces"
1403.5377: Andrej Gendiar, Michal Daniska, Roman Krcmar, Tomotoshi Nishino, "Mean-field universality class induced by weak hyperbolic curvatures"
1310.5898: Daniel Gandolfo, Jean Ruiz, Senya Shlosman, "A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane"
1005.3378: Takatsugu Iharagi, Andrej Gendiar, Hiroshi Ueda, Tomotoshi Nishino, "Phase Transition of the Ising model on a Hyperbolic Lattice"
0906.5523: Yasunori Sakaniwa, Hiroyuki Shima, "Survival of short-range order in the Ising model on negatively curved surfaces"
0807.0150: R. Krcmar, T. Iharagi, A. Gendiar, T. Nishino, "Tricritical point of J1-J2 Ising model on hyperbolic lattice"
0712.0461: Roman Krcmar, Andrej Gendiar, Kouji Ueda, Tomotoshi Nishino, "Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method"
0704.1949: Kouji Ueda, Roman Krcmar, Andrej Gendiar, Tomotoshi Nishino, "Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane"
cond-mat/0612509: Isaku Hasegawa, Yasunori Sakaniwa, Hiroyuki Shima, "Novel scaling behavior of the Ising model on curved surfaces"
cond-mat/0512167: Hiroyuki Shima, Yasunori Sakaniwa, "The dynamic exponent of the Ising model on negatively curved surfaces"
cond-mat/0511539: Hiroyuki Shima, Yasunori Sakaniwa, "Geometric effects on critical behaviours of the Ising model"
hep-th/0404136: Benjamin Doyon, Pedro Fonseca, "Ising Field Theory on a Pseudosphere"
cond-mat/0007398: J.C. Angles d'Auriac, R. Melin, P. Chandra, B. Doucot, "Spin Models on Non-Euclidean Hyperlattices: Griffiths Phases without Extrinsic Disorder"
0009.JSP: C. Chris Wu, "Ising Models on Hyperbolic Graphs II"
9610.JSP: C. Chris Wu, "Ising models on hyperbolic graphs"
9212.IOP: R. Rietman , B. Nienhuis, J. Oitmaa, "The Ising model on hyperlattices"
9003.CMP: C. M. Series, Ya. G. Sinai, "Ising models on the Lobachevsky plane"
7711.TMP: F. Lund, M. Rasetti, T. Regge, "Dimer and Ising models on the Lobachevskii plane"

Clock Model, XY:
1510.02129: Steven Gubser, Zain H. Saleem, Samuel S. Schoenholz, Bogdan Stoica, James Stokes, "Nonlinear Sigma Models with Compact Hyperbolic Target Spaces"
0912.2830: Seung Ki Baek, Petter Minnhagen, Beom Jun Kim, "True and quasi long-range order in the generalized q-state clock model"
0811.1895: Seung Ki Baek, Hiroyuki Shima, Beom Jun Kim, "Curvature-induced frustration in the XY model on hyperbolic surfaces"
0801.0836: Andrej Gendiar, Roman Krcmar, Kouiji Ueda, Tomotoshi Nishino, "Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method"
0706.0044: Seung Ki Baek, Petter Minnhagen, Beom Jun Kim, "Phase Transition of XY Model in Heptagonal Lattice"

Diffusion / Brownian Motion:
1009.3232: C. Vignat, P.W. Lamberti, "An H-theorem for the Brownian motion on the hyperbolic plane"
0807.2089: Seung Ki Baek, Su Do Yi, Beom Jun Kim, "Diffusion on a heptagonal lattice"

Glauber Dynamics:
0712.0489: Alessandra Bianchi, "Glauber dynamics on nonamenable graphs: Boundary conditions and mixing time"
math/0308284: Noam Berger, Claire Kenyon, Elchanan Mossel, Yuval Peres, "Glauber Dynamics on Trees and Hyperbolic Graphs"
math/0307336: Fabio Martinelli, Alistair Sinclair, Dror Weitz, "Glauber dynamics on trees:Boundary conditions and mixing time"

Lattice Structure:
cond-mat/0703326: Francois Sausset, Gilles Tarjus, "Periodic boundary conditions on the pseudosphere"

1D Quantum Systems:
1008.3458: Hiroshi Ueda, Andrej Gendiar, Valentin Zauner, Takatsugu Iharagi, Tomotoshi Nishino, "Transverse Field Ising Model Under Hyperbolic Deformation"
0812.4513: Hiroshi Ueda, Hiroki Nakano, Koichi Kusakabe, Tomotoshi Nishino, "Gap Estimation by means of Hyperbolic Deformation"
0808.3858: Hiroshi Ueda, Tomotoshi Nishino, "Hyperbolic Deformation on Quantum Lattice Hamiltonians"

2D Quantum Systems:
1510.01450: Michal Daniska, Andrej Gendiar, "Analysis of quantum spin models on hyperbolic lattices and Bethe lattice"

Other Topics:
1607.03901: Daniel Harlow, "The Ryu-Takayanagi Formula from Quantum Error Correction"
1606.00621: Arpan Bhattacharyya, Zhe-Shen Gao, Ling-Yan Hung, Si-Nong Liu, "Exploring the Tensor Networks/AdS Correspondence"
1507.02909: Karim Mnasri, Bhilahari Jeevanesan, Jorg Schmalian, "Critical Phenomena in Hyperbolic Space"
1210.0215: Hanno Gottschalk, Horst Thaler, "A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction"
1205.1033: V.R. Misko, Franco Nori, "Magnetic flux pinning in superconductors with hyperbolic-tesselation arrays of pinning sites"
0507.CPC: NEAL MADRAS, C. CHRIS WU, "Self-Avoiding Walks on Hyperbolic Graphs"
1006.5169: Dmitri Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, Marian Boguna, "Hyperbolic Geometry of Complex Networks"
1009.0267: Marian Boguna, Fragkiskos Papadopoulos, Dmitri Krioukov, "Sustaining the Internet with hyperbolic mapping"

See also: Sine Square Deformation

Please contact to nishino@kobe-u.ac.jp about this page.

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