How do you measure numerically central charge of the system ?

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Discussion Overview

The discussion revolves around the numerical measurement of the central charge in a statistical system, particularly in the context of Monte-Carlo simulations at a conformal point. Participants explore the relationship between central charge and observables like free energy and stress-energy tensor, while questioning the existence of systematic methods for measurement in simulations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about methods to numerically appreciate the central charge during Monte-Carlo simulations, noting the connection to free energy and stress-energy tensor but highlighting the lack of direct observables.
  • Another participant discusses methods for measuring electrostatic charge, suggesting techniques involving electroscopes, but does not directly address the central charge issue.
  • There is a repeated emphasis on the need for clarity regarding whether the discussion pertains to measuring electric charge or the central charge of a conformal field theory.

Areas of Agreement / Disagreement

Participants do not appear to agree on the focus of the discussion, with some addressing electrostatic charge measurement while others seek to clarify the measurement of central charge in conformal field theories. The discussion remains unresolved regarding systematic methods for measuring central charge.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the relationship between central charge and other observables, as well as the applicability of electrostatic charge measurement techniques to the central charge context.

Murtuza Tipu
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Let's say that you are doing some Monte-Carlo simulations of a statistical system on a lattice and you observe scale invariance, meaning that you are at a conformal point. Can you get a numerical appreciation of the central charge?

I know how the central charge is related on the free energy (on a cylinder for example) or to the stress-energy tensor but these are not direct observable in a Monte-Carlo.

Is there a systematic method for that? Has it already been done?
 
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Measuring electrostatic charge

Well, theoretical suggestions are as many;
but lab techniques suggest for scaled electroscopes to do as such.
There also are technical issues

Measuring the q charge - contacting method
1) Sure one has to contact the "point" charge with the top head of the electroscope.
2) The scale has to agree with the physical systems of measurements, SI or else.

Measuring the V potential capabilities - induction method
1) Sure one has to keep the "point" charge at several distances with the top head of the electroscope.
2) The scale has to agree with the physical systems of measurements, SI or else.
 
alionalizoti said:
Well, theoretical suggestions are as many;
but lab techniques suggest for scaled electroscopes to do as such.
There also are technical issues

Measuring the q charge - contacting method
1) Sure one has to contact the "point" charge with the top head of the electroscope.
2) The scale has to agree with the physical systems of measurements, SI or else.

Measuring the V potential capabilities - induction method
1) Sure one has to keep the "point" charge at several distances with the top head of the electroscope.
2) The scale has to agree with the physical systems of measurements, SI or else.
Is you answer about measuring an electric charge? I'm interested in 'measuring' numerically the central charge which is a number characterizing a conformal field theory.
 
Measuring the charge

Of course, I mean measuring the electrostatic charge,
which sure be at the center of any net field or field net, whatever!
( any means theoretical or experimental )
 

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