Ising model is an ABM

29 Pages·2017·3.52 MB·English

Agent-based modelling of complex
systems
Janusz Szwabiński
Lecture #4: Simple ABMs
Outlook
The need for ABM
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Applications of ABM
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Note on topologies
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Ising model is an ABM :)
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Forrest fire model
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Schilling model
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El Farol model
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The need for ABM
The problem at hand is too difficult to solve analytically
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An experiment is expensive or not feasible to perform
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An approximate theoretical result needs to be checked
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with a different method
Applications of ABM
Biology: population dynamics,
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spread of epidemics,
threat of biowarfare, ecology,
tissue formation, human immune
system
Business: organizational behavior
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and cognition, team working, supply chain optimization
and logistics, consumer behavior
Technology: traffic congestion, urban planning
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Economics and social sciences: crashes and booms,
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financial markets, opinion formation, cooperation in social
systems
Applications of ABM
Source: http://blogs.casa.ucl.ac.uk/category/netlogo/
Note on topologies
Sometimes spatial interactions are not important (e.g.
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diffusion of opinion on Twitter)
Agents can move in continuous or discrete space
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Agents can be connected by networks of various types
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Grid (Moore Euklidian space Geographic Complex network
neighborhood) (2D and 3D) Information
System (GIS)
Note on topologies
Real networks are complex:
Note on topologies
Models are easier to handle:
Main characteristics of ABM
simple rules can be used to generate complex
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phenomena
randomness in individual behavior can result in consistent
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patterns of population behavior
complex patterns can “self-organize” without any leader
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orchestrating the behavior
different models emphasize different aspects of the world
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Ising model is an ABM :)
invented by Lenz (1920), solved by Ising (1925)
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model of ferromagnetism
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Local interaction
External field
Dynamic rule → spin flip, accepted
with probability:
Agents
Interaction topology
(e.g. square lattice in 2D)