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#
Phase Transition in Hyperbolic Space

**This Page is Under Construction**

**Percolation: **

**Thesis**:
Daan Mulder,
"Percolation and the Ising model in the hyperbolic plane"

**1708.05876**:
Stephan Mertens, Cristopher Moore,
"Percolation Thresholds in Hyperbolic Lattices"

**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.): **

**2210.07227**:
Benedikt Placke, Nikolas P. Breuckmann,
"The Random-Bond Ising Model and its dual in Hyperbolic Spaces"

**1909.12107**:
Nikolas P. Breuckmann, Benedikt Placke, Ananda Roy,
"The Critical Properties of the Ising Model in Hyperbolic Space"

**1707.04183**:
Zhongyang Li,
"Constrained percolation, Ising model and XOR Ising model on planar lattices"

**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: **

**2308.01351**:
Jonathan B. Curtis, Prineha Narang, Victor Galitski,
"Absence of Weak Localization on Negative Curvature Surfaces"

**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: **

**2105.01087**:
Igor Boettcher, Alexey V. Gorshkov, Alicia J. Kollar, Joseph Maciejko, Steven Rayan, Ronny Thomale,
"Crystallography of Hyperbolic Lattices"

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

**1D Quantum Systems: **

**2205.05693**:
Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, Rene Meyer, Zhuo-Yu Xian,
"Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings"

**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: **

**2312.10544**:
Ying-Ying Li, Muhammad Omer Sajid, Judah Unmuth-Yockey,
"Lattice Holography on a Quantum Computer"

**2310.07978**:
Anffany Chen, Joseph Maciejko, Igor Boettcher,
"Anderson localization transition in disordered hyperbolic lattices"

**2306.08248**:
Eric Petermann, Haye Hinrichsen,
"Eigenmodes of the Laplacian on Hyperbolic Lattices"

**2305.19810**:
Junsong Sun, Chang-An Li, Shiping Feng, Huaiming Guo,
"Hybrid higher-order skin-topological effect in hyperbolic lattices"

**2304.03273**:
Anffany Chen, Yifei Guan, Patrick M. Lenggenhager, Joseph Maciejko, Igor Boettcher, Tomas Bzdusek,
"Symmetry and topology of hyperbolic Haldane models"

**2304.02382**:
R. Mosseri, J. Vidal,
"Density of states of tight-binding models in the hyperbolic plane"

**2302.04864**:
Noble Gluscevich, Abhisek Samanta, Sourav Manna, Bitan Roy,
"Dynamic mass generation on two-dimensional electronic hyperbolic lattices"

**2209.02904**:
Zheng-Rong Liu, Chun-Bo Hua, Tan Peng, Rui Chen, Bin Zhou,
"Higher-order topological insulators in hyperbolic lattices"

**2209.02262**:
Yu-Liang Tao, Yong Xu,
"Higher-order Topological Hyperbolic Lattices"

**2206.04543**:
R. Mosseri, R. Vogeler, J. Vidal,
"Aharonov-Bohm cages, flat bands, and gap labelling in hyperbolic tilings"

**2205.11571**:
Tomas Bzdusek, Joseph Maciejko,
"Flat bands and band touching from real-space topology in hyperbolic lattices"

**2203.02101**:
Zheng-Rong Liu, Chun-Bo Hua, Tan Peng, Bin Zhou,
"Chern insulator in a hyperbolic lattice"

**1804.06382**:
Eduardo Brandani da Silva, Waldir Silva Soares Jr,
"Hyperbolic quantum color codes"

**1510.01450**:
Michal Daniska, Andrej Gendiar,
"Analysis of quantum spin models on hyperbolic lattices and Bethe lattice"

**1503.06237**:
Fernando Pastawski, Beni Yoshida, Daniel Harlow, John Preskill,
"Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence"

**Other Topics: **

**2309.10844**:
Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson S. E. Portela, Dietmar Herdt, Felix Dusel,
"Hypertiling -- a high performance Python library for the generation and visualization of hyperbolic lattices"

**2205.05081**:
Pablo Basteiro, Felix Dusel, Johanna Erdmenger, Dietmar Herdt, Haye Hinrichsen, Rene Meyer, Manuel Schrauth,
"Breitenlohner-Freedman bound on hyperbolic tilings"

**2005.12726**:
Muhammad Asaduzzaman, Simon Catterall, Jay Hubisz, Roice Nelson, Judah Unmuth-Yockey,
"Holography on tessellations of hyperbolic space"

**1805.02665**:
Latham Boyle, Ben Dickens, Felix Flicker,
"Conformal Quasicrystals and Holography"

**1802.09549**:
Alicia J. Kollar, Mattias Fitzpatrick, Andrew A. Houck,
"Hyperbolic Lattices in Circuit Quantum Electrodynamics"

**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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