Propagator Fluctuations

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\documentclass[tikz]{standalone}

\usetikzlibrary{patterns}

\tikzset{
  cross/.style={
    path picture={
      \draw[black] (path picture bounding box.south east) -- (path picture bounding box.north west) (path picture bounding box.south west) -- (path picture bounding box.north east);
    }
  }
}

\def\unit{0.7}

\begin{document}

% Diagram 1
\begin{tikzpicture}
  \draw[thick] (0,0) circle (\unit);
  \draw (-2*\unit,0) -- (-\unit,0) (\unit,0) -- (2*\unit,0);
  \draw[fill=white,cross] (0,\unit) circle (0.15*\unit) node[below=2*\unit] {$\partial_k R_k$};

  \draw[fill=white,postaction={pattern=north east lines}] (\unit,0) circle (0.2*\unit) node[above right] {$\Gamma_k^{(3)}$} (-\unit,0) circle (0.2*\unit) node[above left] {$\Gamma_k^{(3)}$};
\end{tikzpicture}

% Diagram 2
\begin{tikzpicture}
  \draw[thick] (0,0) circle (\unit);
  \draw (-2*\unit,0) -- (-\unit,0) (\unit,0) -- (2*\unit,0);
  \draw[fill=white,cross] (0,-\unit) circle (0.15*\unit) node[above=2*\unit] {$\partial_k R_k$};

  \draw[fill=white,postaction={pattern=north east lines}] (\unit,0) circle (0.2*\unit) node[above right] {$\Gamma_k^{(3)}$} (-\unit,0) circle (0.2*\unit) node[above left] {$\Gamma_k^{(3)}$};
\end{tikzpicture}

% Diagram 3
\begin{tikzpicture}
  \draw[thick] (0,0) circle (\unit);
  \draw (-2*\unit,-\unit) -- (2*\unit,-\unit);
  \draw[fill=white,cross] (0,\unit) circle (0.15*\unit) node[below=2*\unit] {$\partial_k R_k$};

  \draw[fill=white,postaction={pattern=north east lines}] (0,-\unit) circle (0.2*\unit) node[above=3*\unit] {$\Gamma_k^{(4)}$};
\end{tikzpicture}

\end{document}

#import "@preview/cetz:0.4.1": canvas, draw
#import "@preview/modpattern:0.1.0": modpattern
#import draw: circle, content, group, line, rect

#set page(width: auto, height: auto, margin: 8pt)

// TODO fix hatches rendering as black fill https://github.com/cetz-package/cetz/issues/805#issuecomment-2629554884
#let hatched = modpattern(
  (.1cm, .1cm),
  std.line(start: (0%, 100%), end: (100%, 0%), stroke: 0.5pt),
  background: white,
)

#canvas({
  // Define styles and constants
  let unit = 1
  let vertex-radius = 0.2 * unit
  let cross-radius = 0.15 * unit
  let ext-len = 2 * unit

  // Helper function for cross markers
  let cross(pos, label: none, label-offset: 2, rel-label: (0, -0.5)) = {
    let rad = cross-radius
    content(pos, text(size: 16pt)[$times.circle$], stroke: none, fill: white, frame: "circle", padding: -2.5pt)
    if label != none {
      content((rel: rel-label, to: pos), eval(label, mode: "math"))
    }
  }

  // Helper function for hatched vertices
  let vertex(pos, label: none, rel-label: (0.35, 0.35)) = {
    circle(pos, radius: vertex-radius, fill: hatched)

    if label != none {
      content((rel: rel-label, to: pos), eval(label, mode: "math"))
    }
  }

  // Diagram 1
  group(name: "diagram1", {
    // Main circle
    circle((0, 0), radius: unit, stroke: 1pt)

    // External lines
    line((-ext-len, 0), (-unit, 0), stroke: 1pt)
    line((unit, 0), (ext-len, 0), stroke: 1pt)

    // Cross marker
    cross((0, unit), label: "partial_k R_k")

    // Vertices
    vertex((-unit, 0), label: "Gamma_k^(3)", rel-label: (-0.35, 0.35))
    vertex((unit, 0), label: "Gamma_k^(3)")
  })

  // Diagram 2
  group(name: "diagram2", {
    // Move right by 5 units
    let offset = (5, 0)

    // Main circle
    circle((offset.at(0), 0), radius: unit, stroke: 1pt)

    // External lines
    line((-ext-len + offset.at(0), 0), (-unit + offset.at(0), 0), stroke: 1pt)
    line((unit + offset.at(0), 0), (ext-len + offset.at(0), 0), stroke: 1pt)

    // Cross marker
    cross((offset.at(0), -unit), label: "partial_k R_k", rel-label: (0, 0.5))

    // Vertices
    vertex((-unit + offset.at(0), 0), label: "Gamma_k^(3)", rel-label: (-0.35, 0.35))
    vertex((unit + offset.at(0), 0), label: "Gamma_k^(3)")
  })

  // Diagram 3
  group(name: "diagram3", {
    // Move right by 10 units
    let offset = (10, 0)

    // Main circle
    circle((offset.at(0), 0), radius: unit, stroke: 1pt)

    // External line
    line(
      (-ext-len + offset.at(0), -unit),
      (ext-len + offset.at(0), -unit),
      stroke: 1pt,
    )

    // Cross marker
    cross((offset.at(0), unit), label: "partial_k R_k")

    // Vertex
    vertex((offset.at(0), -unit), label: "Gamma_k^(4)")
  })
})