All Questions
Tagged with renormalization ising-model
43
questions
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23
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Scaling equation for the external field H in an Ising like system [closed]
i want to show that the following relation is true for the external field H, starting from the scaling form of the free energy. It is an Ising like System close to a critical point with $M \geq 0$ and ...
- 43
2
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1
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47
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Why does integrating out microscopic degrees of freedom lead to the effective free energy rather than the effective energy?
In David Tong's lecture notes on statistical field theory, he considers the partition function of the Ising model and computes the effective free energy by integrating out the microscopic details of ...
- 23
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55
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Using the RG equations to find the free energy scaling form of the 2D Ising Model
i am trying to calculate the scaling form of the free energy of the 2D Ising model, starting from it's RG equations:
$$\frac{d u_I}{dl} = 2 u_I + u_t^2$$
$$\frac{d u_t}{dl} = u_t$$
$$\frac{d u_h}{dl} =...
- 43
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85
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Gaussian approximation of Landau Ginzburg and Renoramalization Group
I am studing an introduction to the Renormalization Group (RG); during my course my prof. came up saying that:
Landau-Ginzburg (LG) theory truncated at Gaussian order is exact at the critical point.
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139
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Depicting the renormalization group in terms of decimation and rescaling
In this paper, the author is discussing the renormalization group, as done with the Ising model.
Some aspects of the description don't seem to make sense, though I must be misunderstanding something. ...
- 101
2
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1
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74
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Is flowing with RG in 1D Ising model equivalent to changing the temperature of the system
Let us consider the easiest form of the Ising Hamiltonian:
$$ \beta H(s_i; J) = -J\sum_i^N s_i s_{i+1} $$ ($\beta = 1/k_BT$ so we already defined $J = \tilde{J}/k_BT$ with $\tilde{J}$ constant).
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- 97
1
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110
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Extra term in $2+\epsilon$ expansion of sigma model
I'm working through David Tong's notes on Statistical Field Theory, in particular the $2+\epsilon$ expansion of the sigma model with free energy
$$F[\vec{n}]=\int d^dx \frac{1}{2e^2}\nabla\vec{n}\cdot\...
- 248
2
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1
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255
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How renormalization allows to describe critical point behaviour using the critical fixed point?
As in the title, I am trying to understand how the critical fixed point (CFP) can be used to derive the thermodynamic singular behavior of the physical critical point (PCP). The context I have in mind ...
- 823
1
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1
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115
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Reference request: readable introduction to Landau theory and phase transition
I am doing some self-study on Landau theory and phase transition models in physics. In particular I am looking at how to apply these ideas to opinion dynamics models. I found a really nice set of ...
5
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1
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556
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Interpretation of Renormalization Group
For the purposes of this question, I will be talking about systems in statistical mechanics (e.g the Ising Model) so I will assume the system of interest has a natural cutoff frequency $\Lambda$.
For ...
- 1,778
1
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40
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Scaling of "non-reduced" parameters in RG theory
I'm studying quantum phase transitions using the Renormalization Group (RG) method. In Continentino's book "Quantum Scaling in Many-Body Systems: An Approach to Quantum Phase Transitions" ...
- 1,396
1
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1
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139
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Applications of real-space renormalizaton group (RG)
I'm looking for lattice models on which real-space RG can be applied fairly simply to get decent results. In particular, I'm looking for something like the classical 2D Ising model on a triangular ...
3
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0
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163
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Why do the critical exponents at the Gaussian fixed point coincide with mean field theory?
In the Ising model, we know that in dimensions higher than the upper critical dimension, $d_u=4$, the critical exponents can be found from mean field theory. We also know that for the same dimensions, ...
- 857
2
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1
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120
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Ising universallity class on triangular lattice
Is Ising universallity class on triangular or hexagonal lattice different from universallity class on rectangular lattice?
Is universallty class depends on type of microscopical graph or topology on ...
- 5,707
2
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0
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386
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Does the 3D Ising model violate the hyperscaling relation?
The hyperscaling relation relates two critical exponents $\{\alpha,\nu\}$ (the power the divergence of the specific heat $c$ and correlation length $\zeta$ near a critical temperature $T_c$) as ...
- 713