the ising spin lattice model
play

The Ising Spin Lattice Model Alexander Brunmayr Graduate mentor: - PowerPoint PPT Presentation

Dec 08, 2022 •150 likes •286 views

The Ising Spin Lattice Model Alexander Brunmayr Graduate mentor: Nicholas Paskal & Stephen Sorokanich August 28, 2018 Mini Physics Intro Course Magnets and spins, magnetization Ferromagnetism Spins under an external magnetic field Ising

  1. The Ising Spin Lattice Model Alexander Brunmayr Graduate mentor: Nicholas Paskal & Stephen Sorokanich August 28, 2018

  2. Mini Physics Intro Course Magnets and spins, magnetization Ferromagnetism Spins under an external magnetic field

  3. Ising Nearest-Neighbor Lattice Model Models a ferromagnetic (or antiferromagnetic) material Only nearest-neighbor interactions Square Lattice with periodic boundary conditions

  4. 1D Ising Model We want to predict the magnetization of the system where

  5. 1D Ising Model

  6. 1D Ising Model Critical behavior at T=0

  7. 2D Ising Model Phase transition for temperatures below the Curie Temperature (Tc > 0) T > Curie Temperature: T = Curie Temperature no phase transition T < Curie Temperature: phase transition

  8. 2D Ising Model

  9. 3D and Beyond No analytical solution for dimensions 3 and higher Numerical solutions (see computer simulations)

  10. Simulations Step 1: select a location at random Step 2: ● Metropolis Algorithm: ○ if Energy decreases → flip spin ○ if Energy increases → flip spin with probability e – β ΔE ● Glauber Algorithm: ○ Flip spin with probability 1/(1+e β ΔE ) ● Voter Algorithm: ○ Set spin to be like a randomly selected neighbor

  11. Applications Magnets Neurology Computer science Solar magnetograms

  12. Texts and Sources R.J. Baxter : Exactly Solved Models in Statistical Mechanics R.A. Minlos : Introduction to Mathematical Statistical Physics (Lecture Series) Linda E. Reichl : A Modern Course in Statistical Physics (4th ed.) D.A. Levin : Glauber Dynamics for Ising Model I (AMS Short Course, UOregon) Raissa D’Souza : Simulating Glauber Dynamics for the Ising Model (UC Davis)

Recommend

1D Ising model Simple model of interacting spins in a lattice Nearest-neighbor only No

1D Ising model Simple model of interacting spins in a lattice Nearest-neighbor only No

1D Ising model Simple model of interacting spins in a lattice Nearest-neighbor only No external magnetic field Here, we look at a 1D chain of spins Future: higher dimensions, higher coordination numbers Numerical Challenge

370 views • 4 slides
Monte Carlo simulations of the 2D Ising model Stochastic sampling of spin configurations to

Monte Carlo simulations of the 2D Ising model Stochastic sampling of spin configurations to

Monte Carlo simulations of the 2D Ising model Stochastic sampling of spin configurations to estimate Spin configurations configurations; can sample very small fraction for large N Trivial Monte Carlo sampling fails at low T, because the sum is

332 views • 15 slides
Spin-charge order in Kondo-Lattice Model on triangular lattice Sanjeev Kumar Indian Institute of

Spin-charge order in Kondo-Lattice Model on triangular lattice Sanjeev Kumar Indian Institute of

Spin-charge order in Kondo-Lattice Model on triangular lattice Sanjeev Kumar Indian Institute of Science Education and Research (IISER) Mohali INDIA arXiv:1412.2319 Frustrated Magnetism @ JNU Feb. 10, 2015 In

785 views • 27 slides
Monte Carlo simulation of the 2D Ising model - tutorial - Zoltn Nda Babe-Bolyai University

Monte Carlo simulation of the 2D Ising model - tutorial - Zoltn Nda Babe-Bolyai University

Monte Carlo simulation of the 2D Ising model - tutorial - Zoltn Nda Babe-Bolyai University Department of Theoretical and Computational Physics . A basic Metropolis Algorithm for simulating the 2D and 3D Ising model on square lattice

462 views • 8 slides
Ising model with random boundary condition A. C. D. van Enter # , K. Neto y &amp; , and H. G.

Ising model with random boundary condition A. C. D. van Enter # , K. Neto y &amp; , and H. G.

Equilibrium and Dynamics of Spin Glasses Monte Verita, April 18-23, 2004 Ising model with random boundary condition A. C. D. van Enter # , K. Neto y &amp; , and H. G. Schaap # cn # Institute for Theoretical Physics R.U.G. Groningen, The

473 views • 9 slides
Quantum Integer Programming 47-779 Ising Model 1 William Larimer Mellon, Founder Agenda o

Quantum Integer Programming 47-779 Ising Model 1 William Larimer Mellon, Founder Agenda o

Quantum Integer Programming 47-779 Ising Model 1 William Larimer Mellon, Founder Agenda o Ising Model: Background, Physics o Ising Model: Solutions o Ising Model and Combinatorial Optimization o Ising Model and Integer Programming o Solving

669 views • 19 slides
Circle patterns and critical Ising models Marcin Lis February 18, 2019 1 / 13 Can we compute

Circle patterns and critical Ising models Marcin Lis February 18, 2019 1 / 13 Can we compute

Circle patterns and critical Ising models Marcin Lis February 18, 2019 1 / 13 Can we compute the critical point of the Ising model? For d = 1, c = (Ising 25). For d = 2, we have many examples: square lattice biperiodic

481 views • 27 slides
Cluster algorithm for the Ising model Define bond index corresponding to pair of interacting spins

Cluster algorithm for the Ising model Define bond index corresponding to pair of interacting spins

Cluster algorithm for the Ising model Define bond index corresponding to pair of interacting spins Number of bonds N b = dN for a d-dimensional cubic lattice Write the energy of the Ising ferromagnet as Write the partition function as Define

302 views • 14 slides
Using multiple SLE to explain a certain observable in the 2d Ising model Michael J. Kozdron

Using multiple SLE to explain a certain observable in the 2d Ising model Michael J. Kozdron

Using multiple SLE to explain a certain observable in the 2d Ising model Michael J. Kozdron University of Regina http://stat.math.uregina.ca/ kozdron/ Statcomb 2009: Workshop on Two-Dimensional Lattice Models Centre Emile Borel, Institut

499 views • 36 slides
Height representation of XOR-Ising loops via bipartite dimers C edric Boutillier (UPMC) B

Height representation of XOR-Ising loops via bipartite dimers C edric Boutillier (UPMC) B

Height representation of XOR-Ising loops via bipartite dimers C edric Boutillier (UPMC) B eatrice de Tili` ere (UPMC) LAGA Universit e Paris Nord March 11, 2015 The Ising model and the XOR-Ising model The Ising model Let G =

797 views • 43 slides
A power-law upper bound on the correlations in the two-dimensional random-field Ising model Ron

A power-law upper bound on the correlations in the two-dimensional random-field Ising model Ron

A power-law upper bound on the correlations in the two-dimensional random-field Ising model Ron Peled, Tel Aviv University Based on a joint work with Michael Aizenman, Princeton ICMP 2018, Montreal Random-field Ising model Standard Ising

447 views • 12 slides
Ising superconductivity in gated MoS2 17.12.15

Ising superconductivity in gated MoS2 17.12.15

Ising superconductivity in gated MoS2 17.12.15 Background Ising superconductor (Zeeman-protected superconductor): Intrinsic spin-orbit coupling induced effective Zeeman field with

1.22k views • 32 slides
Some results on two-dimensional anisotropic Ising spin systems and percolation Maria Eul alia

Some results on two-dimensional anisotropic Ising spin systems and percolation Maria Eul alia

Some results on two-dimensional anisotropic Ising spin systems and percolation Maria Eul alia Vares UFRJ, Rio de Janeiro Based on joint paper / work in progress with L.R. Fontes, D. Marchetti, I. Merola, E. Presutti / T. Mountford

239 views • 21 slides
The critical Z -invariant Ising model via dimers B eatrice de Tili` ere University of

The critical Z -invariant Ising model via dimers B eatrice de Tili` ere University of

The critical Z -invariant Ising model via dimers B eatrice de Tili` ere University of Neuch atel joint work with C edric Boutillier, University Paris 6 Ascona, 27 May 2010 The 2 -dimensional Ising model Planar graph, G = ( V ( G )

600 views • 24 slides
1st PRIMA Congress Conformal invariance and universality in the 2D Ising model Stanislav Smirnov

1st PRIMA Congress Conformal invariance and universality in the 2D Ising model Stanislav Smirnov

1st PRIMA Congress Conformal invariance and universality in the 2D Ising model Stanislav Smirnov July 6, 2009 Archetypical example of a phase transition: 2D Ising model Configurations of + and spins (red and blue squares) Prob( config )

669 views • 31 slides
SLE and conformal invariance for critical Ising model Stanislav Smirnov jointly with Dmitry

SLE and conformal invariance for critical Ising model Stanislav Smirnov jointly with Dmitry

3rd LA PIETRA WEEK IN PROBABILITY Stochastic Models in Physics Firenze, June 23-27, 2008 SLE and conformal invariance for critical Ising model Stanislav Smirnov jointly with Dmitry Chelkak 1D Ising model 0 1

355 views • 20 slides
Crossing probabilities in the critical 2D Ising model Dmitry Chelkak (PDMI Steklov, St.Petersburg)

Crossing probabilities in the critical 2D Ising model Dmitry Chelkak (PDMI Steklov, St.Petersburg)

Crossing probabilities in the critical 2D Ising model Dmitry Chelkak (PDMI Steklov, St.Petersburg) joint work with Stanislav Smirnov (Geneva) arXiv:0910.2045 : Universality in the 2D Ising model and conformal invariance of fermionic

667 views • 42 slides
Planar Ising model at criticality: state-of-the-art and perspectives Dmitry Chelkak, ENS,

Planar Ising model at criticality: state-of-the-art and perspectives Dmitry Chelkak, ENS,

Planar Ising model at criticality: state-of-the-art and perspectives Dmitry Chelkak, ENS, Paris [ &amp; PDMI, St. Petersburg (on leave) ] ICM, Rio de Janeiro, August 4, 2018 Planar Ising model at criticality: outline Combinatorics

791 views • 37 slides
Ising Model and Percolation Problem Shahin Rouhani Physics Department Sharif University of

Ising Model and Percolation Problem Shahin Rouhani Physics Department Sharif University of

Statistical Mechanics of Two Dimensional Critical Curves Ising Model and Percolation Problem Shahin Rouhani Physics Department Sharif University of Technology Tehran, Iran. Scale invariance in the critical Ising model Let us illustrate

394 views • 27 slides
Hypergeometric SLE and Convergence of Multiple Interfaces in Lattice Models Hao Wu Yau

Hypergeometric SLE and Convergence of Multiple Interfaces in Lattice Models Hao Wu Yau

Hypergeometric SLE and Convergence of Multiple Interfaces in Lattice Models Hao Wu Yau Mathematical Sciences Center, Tsinghua University, China Hao Wu (THU) Hypergeometric SLE 1 / 32 Background Table of contents Background 1 Ising model

437 views • 31 slides
Convergence of correlations in the 2D Ising model: primary fields [ and the stress-energy tensor

Convergence of correlations in the 2D Ising model: primary fields [ and the stress-energy tensor

Convergence of correlations in the 2D Ising model: primary fields [ and the stress-energy tensor ] Dmitry Chelkak [ ENS, Paris &amp; Steklov Institute, St. Petersburg ] [ Sample of a critical 2D Ising configuration (with two disorders), c

1.24k views • 54 slides
Quantum Spin Liquid of the Kagome- and Triangular-Lattice Antiferromagnets and Related Materials

Quantum Spin Liquid of the Kagome- and Triangular-Lattice Antiferromagnets and Related Materials

YIPQS long-term and Nishinomiya-Yukawa memorial workshop Novel Quantum States in Condensed Matter 2017 at Kyoto on Oct. 23- Nov. 24., 2017 Quantum Spin Liquid of the Kagome- and Triangular-Lattice Antiferromagnets and Related Materials - Spin

459 views • 28 slides
Ising model and total positivity Pavel Galashin MIT galashin@mit.edu University of Toronto

Ising model and total positivity Pavel Galashin MIT galashin@mit.edu University of Toronto

Ising model and total positivity Pavel Galashin MIT galashin@mit.edu University of Toronto Colloquium, January 7, 2019 Joint work with Pavlo Pylyavskyy arXiv:1807.03282 Pavel Galashin (MIT) Ising model and total positivity U of Toronto,

2.08k views • 176 slides
Ising model and total positivity Pavel Galashin MIT galashin@mit.edu University of Michigan,

Ising model and total positivity Pavel Galashin MIT galashin@mit.edu University of Michigan,

Ising model and total positivity Pavel Galashin MIT galashin@mit.edu University of Michigan, October 19, 2018 Joint work with Pavlo Pylyavskyy arXiv:1807.03282 Pavel Galashin (MIT) Ising model and total positivity UMich, 10/19/2018 1 / 32

2.05k views • 186 slides

More recommend